# Download PROBABILITY 4 - STA411 Past Question PDF

You will find PROBABILITY 4 past question PDF which can be downloaded for FREE on this page. PROBABILITY 4 is useful when preparing for STA411 course exams.

PROBABILITY 4 past question for the year 2019 examines 400-level Science and Technology students of FUTO, offering STA411 course on their knowledge of probability, equality, space, central limit theorem, chebyshev's inequality

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## Past Questions related to PROBABILITY 4

Year: 2019

School: University of Nigeria, Nsukka

Department: Science and Technology

Course Code: MTH321

Topics: Metric Space Topology, metric space, discrete metric space, Lipschitz function, Contraction Mapping Principle, nonempty set, set

Year: 2018

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: STA211

Topics: probability, frequency, data plane, scattergram, area plot, histogram, class boundaries, regression, skewness

Year: 2018

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: STA212

Topics: probability, random, distribution, marginal

Year: 2019

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: STA211

Topics: ASYMMETRY, Distrubtion, mean, median, mode, central tendency, frequency distribution, quartile

Year: 2019

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: MTH403

Topics: topology, set, topological space, metric space, open function, discrete topology, discrete space, subspace topology, topological space

Year: 2017

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: random variable, probability distribution, binomial experiment, binomial probabilities, geometric distribution, Poisson distribution, binomial distribution

Year: 2018

School: University of Ilorin

Department: Science and Technology

Course Code: STA121

Topics: permutation, combination

Year: 2018

School: University of Ilorin

Department: Science and Technology

Course Code: MAT326

Topics: Laurent expansion, Liouville theorem, Residue Theorem, Cauchy inequality, Rouche theorem, Analytic continuation, convergence, maximum modulus theorem

Year: 2018

School: University of Ilorin

Department: Science and Technology

Course Code: MAT322

Topics: Set

Year: 2018

School: University of Ilorin

Department: Science and Technology

Course Code: MAT332

Topics: Jacobi, Gauss seidel, Chebyshev form, Romberg integration, Natural spline, Orthogonal polynomial, Gram-shmidt, Trapezoidal rule, Simpson rule, metric space

Year: 2018

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: MTH101

Topics: logarithm, partial fraction, inequality, linear expansion, complex number, arithmetic progression, geometric progression

Year: 2020

School: University of Benin

Department: Science and Technology

Course Code: MTH112

Topics: Function limit, continuity, differentiation, product rule theorem

Year: 2019

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: BTC301

Topics: biostatics, mean, median, probability, statistics

Year: 2018

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: URP204

Topics: histogram, distribution, standard deviation, probability, statistics

### Books related to PROBABILITY 4

Author: Michael Evans, Jeffrey Rosenthal

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: STA301

Topics: probability models, Conditional Probability, Venn diagram, Random Variables, Discrete Distributions, Continuous Distributions, Cumulative Distribution Functions, Joint Distributions, Simulating Probability Distributions, expectation, Inequalities, Jensen’s Inequality, Sampling Distributions, Limits, Central Limit Theorem, Monte Carlo Approximations, Normal Distribution Theory, Chi-Squared Distribution, Statistical Inference, statistical model, Data Collection, Finite Populations, Simple Random Sampling, Histograms, Survey Sampling, Descriptive Statistics, Plotting Data, Likelihood Inference, Maximum Likelihood Estimation, Distribution-Free Methods, Bayesian Inference, Bayesian Computations, Optimal Inferences, Optimal Unbiased Estimation, Optimal Hypothesis Testing, quantitative response, Simple Linear Regression Model, Bayesian Simple Linear Model, Multiple Linear Regression Model, Markov Chains, Gambler’s Ruin Problem, Markov Chain Monte Carlo, Martingales, Brownian Motion, Poisson Processes

Author: GN Amahia

School: University of Ibadan

Department: Science and Technology

Course Code: STA211

Topics: Probability, Permutations, Combinations, probability laws, conditional Probability, independence rule, Bayes rule, random variables, Chebyshev's inequality, Bernoulli distribution, Binomial Probability distribution, Negative binomial distribution, geometric distribution, Poisson distribution, hypergeometric distribution, uniform distribution, rectangular distribution, normal distribution, Joint marginal distribution, conditional distribution, Gamma distribution, Chi-square distribution

Author: Achim Klenke

School: University of Ilorin

Department: Science and Technology

Course Code: STA121, STA221, ACC401, BUS426, ECN104, ECN207, MEE442, PHY432, AEF204

Topics: measure theory, independence, integral, moments, laws of large numbers, convergence theorem, Lp-Spaces, Radon–Nikodym Theorem, Conditional Expectations, martingale, optional sampling theorem, Martingale Convergence Theorem, Backwards Martingale, exchangeability, De Finetti's theorem, convergence of measures, Characteristic Function, Central Limit Theorem, Infinitely Divisible Distribution, markov chains, Electrical Network, Ergodic Theory, Brownian motion, iterated logarithm, large deviations, Poisson point process, Itô Integral, Stochastic Differential Equations

Author: Steven Kay

School: University of Ilorin

Department: Science and Technology

Course Code: MAT214, MAT335, PHY416, ELE576

Topics: computer simulation, probability, conditional probability, discrete random variables, conditional probability, mass functions, Discrete N-Dimensional Random Variables, Conditional Probability Density Functions, Continuous N-Dimensional Random Variables, Moment Approximations, limit theorem, MATLAB, random process, Wide Sense Stationary Random Process, linear system, Gaussian Random Process, Poisson Random Process, markov chains

Author: CE Chidume, Chukwudi Chidume

School: Federal University of Technology, Owerri

Department: Science and Technology

Course Code: MTH301

Topics: real number system, order relation, natural numbers, countable sets, uncountable sets, bounded sets, limits, Monotone Sequences, Sandwich Theorem, limit theorems, Bolzano-Weierstrass Theorem, Limit Superior, Limit Inferior, Cauchy Sequences, continuity, topological notions, One-sided Continuity, Continuity Theorems, Uniform Continuity, Uniform Continuity Theorems, closed sets, compact sets, continuous maps, differentiability, derivative, Rolle’s Theorem, Mean Value Theorem, L’Hospital’s Rule, Nonnegative Real Numbers series, Integral Test, Comparison Test, Limit Comparison Test, Cauchy’s Root Test, D’Alembert’s Ratio Test, Alternating Series, Absolute Convergence, Conditional Convergence, Riemann Integral, Integration, Uniform convergence, Power Series, Equicontinuity, Arzela-Ascoli Theorem

Author: John Freund, Benjamin Perles

School: University of Ibadan

Department: Science and Technology

Course Code: STA121

Topics: statistics, summarizing data, listing, grouping, Numerical data, Stem-and-Leaf Displays, frequency distribution, graphical presentations, Summarizing Two-Variable Data, population, sample, mean, weighted mean, median, mode, grouped data, measures of variation, range, standard deviation, variance, posibility, probability, counting, permutation, combination, sample spaces, events, odds, conditional probability, multiplication rules, Bayes theorem, Mathematical Expectation, expectation, decision, decision making, Statistical Decision Problems, Random Variable, probability distributions, binomial distributions, hypergeometric distributions, Poisson distribution, Multinomial distribution, Mean of a Probability Distribution, Standard Deviation of a Probability Distribution, normal distribution, Continuous Distributions, sampling, random sampling, sample designs, systematic sampling, stratified sampling, cluster sampling, sampling distribuions, central limit theorem, estimation, Tests of Hypotheses, Significance Tests, One-Way Analysis of Variance, analysis of variance, Multiple Comparisons, Two-Way Analysis of Variance, Design of Experiments, Design of Experiments, regression, Curve Fitting, Regression Analysis, Multiple Regression, Nonlinear Regression, Coefficient of Correlation, correlation, Correlation Analysis, Multiple Correlation, Partial Correlation, Nonparametric tests, sign test, signed-rank test, U test, H test, Tests of Randomness, Rank Correlation

Author: Favour

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: mean of random variable, variance of random variable, continuous random variable, probability density function, probability distribution function, mean continuous of random variable, variance continuous of random variable, discrete distribution, Bernoulli distribution, binomial distribution, Poisson distribution, geometric distribution, uniform distribution, continuous distribution, normal distribution, cumulative distribution function, Bivariate probability distribution, conditional probability distribution function

Author: KK Gan

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: Gaussian Probability Distribution, Binomial distribution, Poisson distribution, Central Limit Theorem

Author: John Schiller, Alu Srinivasan, Murray Spiegel

School: Federal University of Technology, Minna

Department: Science and Technology

Course Code: STA117

Topics: Probability, statistics, Random Variables, Probability Distributions, Mathematical Expectation, Special Probability Distributions, Sampling Theory, Estimation Theory, Curve Fitting, Regression, Correlation, Analysis of Variance, Nonparametric Tests, Bayesian Methods

Author: Douglas Montgomery, George Runger

School: Bayero University, Kano

Department: Engineering

Course Code: EGR4201

Topics: Applied Statistics, Probability, collecting engineering data, sample spaces, event, counting techniques, conditional probability, Baye's theorem, Random variables, discrete random variables, probability distributions, probability mass functions, cumulative distribution functions, Discrete Uniform Distribution, binomial distribution, Hypergeometric Distribution, Poisson Distribution, probability density functions, continuous uniform distribution, Normal distribution, Erlang distributions, Weibull distribution, Lognormal distribution, joint probability distributions, covariance, correlation, probability plots, descriptive statistics, point estimation, statistical inference, multiple linear regression, multiple linear regression model, simple linear regression, analysis of variance

Author: Alexander McFarlane Mood, Franklin Graybill, Duane Boes

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: probability, random variables, distribution function, expectation, moments, chebyshev inequality, Jensen inequality, univariate distribution, discrete distribution, continuous distribution, comments, joint distribution function, conditional distribution, stochastic independence, covariance, correlation, distribution of function, sampling, sampling distribution, sample mean, order statistics, parametric point estimation, point estimators, sufficiency, unbiased estimation, location invariance, scale invariance, Bayes estimator, vector of parameters, parametric interval estimation, confidence interval, test of hypothesis, loss function, Chi-square test, linear model, Nonparametric method, tolerance limit

Author: Alexander McFarlane Mood, Franklin Graybill, Duane Boes

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: probability, random variables, distribution function, expectation, moments, chebyshev inequality, Jensen inequality, univariate distribution, discrete distribution, continuous distribution, comments, joint distribution function, conditional distribution, stochastic independence, covariance, correlation, distribution of function, sampling, sampling distribution, sample mean, order statistics, parametric point estimation, point estimators, sufficiency, unbiased estimation, location invariance, scale invariance, Bayes estimator, vector of parameters, parametric interval estimation, confidence interval, test of hypothesis, loss function, Chi-square test, linear model, Nonparametric method, tolerance limit

Author: Robert Hogg, Joseph McKean, Allen Craig

School: Federal University of Agriculture, Abeokuta

Department: Science and Technology

Course Code: STS213

Topics: Statistics, Probability, Distributions, Multivariate Distributions, statistical inference, consistency, limiting distributions, maximum likelihood methods, sufficiency, optimal test of hypotheses, nonparametric statistics, robust statistics, Bayesian statistics, conditional probability, random variables, correlation coefficient, binomial distribution, Poisson distribution, Normal distribution, Multivariate normal distribution, sampling, confidence intervals, hypothesis testing, central limit theorem, maximum likelihood estimation, sequential probability ratio test, likelihood ratio test, sample median, signed-rank Wilcoxon, Mann–Whitney–Wilcoxon Procedure, Simple Linear Model, Bayesian Procedures

Author: Allen Craig, Robert Hogg, Joseph McKean

School: Federal University of Agriculture, Abeokuta

Department: Science and Technology

Course Code: STS213

Topics: Statistics, Probability, Distributions, Multivariate Distributions, statistical inference, consistency, limiting distributions, maximum likelihood methods, sufficiency, optimal test of hypotheses, nonparametric statistics, robust statistics, Bayesian statistics, conditional probability, random variables, correlation coefficient, binomial distribution, Poisson distribution, Normal distribution, Multivariate normal distribution, sampling, confidence intervals, hypothesis testing, central limit theorem, maximum likelihood estimation, sequential probability ratio test, likelihood ratio test, sample median, signed-rank Wilcoxon, Mann–Whitney–Wilcoxon Procedure, Simple Linear Model, Bayesian Procedures

Author: Michael de Smith

School: University of Ibadan

Department: Science and Technology

Course Code: STA231, STA322, STA351, STA415

Topics: Statistical Analysis, statistical data, statistical method, sampling, sample size, data preparation, data cleaning, missing data, data errors, statistical error, probability theory, odds, risk, frequentist probability theory, Bayesian probability theory, probability distribution, statistical modelling, computational statistics, inference, bias, confounding, hypothesis testing, statistical significance, confidence intervals, Non-parametric analysis, descriptive statistics, measures of central tendency, statistical indices, key functions, matrix, data transformation, data standardization, Box-cox, power transforms, Freeman-turkey transform, log transform, exponential transforms, logit transform, Normal transform, Z-transform, data exploration, graphic, visualization, exploratory data analysis, randomness, randomization, random numbers, random permutations, correlation, autocorrelation, probability distributions, eestimations, estimators, Maximum likelihood estimation, Bayesian estimation, z-test, T-test, variance test, contigency tables, randomized block designs, factorial designs, Analysis of variance, Analysis of covariance, ANOVA, MANOVA, ANCOVA, regression, smoothing, time series analysis

Author: Irwin Miller, Marylees Miller

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: probability, Probability Distribution, Probability Densitiy, Mathematical Expectation, Special Probability Distribution, Special Probability Density, Random Variables, Sampling Distributions, Decision Theory, Point Estimation, Interval Estimation, Hypothesis Testing, Regression, Correlation

Author: Irwin Miller, Marylees Miller

School: University of Ilorin

Department: Science and Technology

Course Code: STA124

Topics: probability, Probability Distribution, Probability Densitiy, Mathematical Expectation, Special Probability Distribution, Special Probability Density, Random Variables, Sampling Distributions, Decision Theory, Point Estimation, Interval Estimation, Hypothesis Testing, Regression, Correlation

Author: GeorgeThomas, Joel Hass, Christopher Heil, Maurice Weir

School: University of Ilorin

Department: Science and Technology

Course Code: MAT112

Topics: Calculus, Trigonometric Functions, functions, limits, continuity, One-Sided Limits, Differentiation Rules, Derivatives, chain rule, implict differentiation, related rates, linearization, differentials, Mean Value Theorem, integrals, Monotonic Functions, First Derivative Test, Concavity, Curve Sketching, Applied Optimization, antiderivatives, Sigma Notation, limits of Finite Sums, Definite integral, Transcendental Functions, inverse functions, natural logarithms, exponential functions, exponential change, seperable differential equation, Indeterminate Form, L’Hôpital’s Rule, Inverse Trigonometric Functions, Hyperbolic Functions, Integration by Parts, integration, trigonometric integrals, trigonometric substitution, Integral Tables, Computer Algebra Systems, probability, numerical integration, improper integrals, probability, First-Order Differential Equations, Slope Fields, Euler’s Method, First-Order Linear Equations, Infinite Sequences, infinite Series, integral test, comparison test, absolute convergence, power series, alternating series, Taylor series, Maclaurin series, Parametric Equations, Polar Coordinates, Conic Sections, vector, Partial Derivatives, Lagrange Multipliers, Multiple Integrals, vector fields, Path Independence, Conservative Fields, Potential Functions, Green’s Theorem, Surface Integrals, Stokes Theorem, Divergence Theorem

Author: Elka Block, Frank Purcell

School: University of Ilorin

Department: Science and Technology

Course Code: MAT112

Topics: Calculus, Trigonometric Functions, functions, limits, continuity, One-Sided Limits, Differentiation Rules, Derivatives, chain rule, implict differentiation, related rates, linearization, differentials, Mean Value Theorem, integrals, Monotonic Functions, First Derivative Test, Concavity, Curve Sketching, Applied Optimization, antiderivatives, Sigma Notation, limits of Finite Sums, Definite integral, Transcendental Functions, inverse functions, natural logarithms, exponential functions, exponential change, seperable differential equation, Indeterminate Form, L’Hôpital’s Rule, Inverse Trigonometric Functions, Hyperbolic Functions, Integration by Parts, integration, trigonometric integrals, trigonometric substitution, Integral Tables, Computer Algebra Systems, probability, numerical integration, improper integrals, probability, First-Order Differential Equations, Slope Fields, Euler’s Method, First-Order Linear Equations, Infinite Sequences, infinite Series, integral test, comparison test, absolute convergence, power series, alternating series, Taylor series, Maclaurin series, Parametric Equations, Polar Coordinates, Conic Sections, vector, Partial Derivatives, Lagrange Multipliers, Multiple Integrals, vector fields, Path Independence, Conservative Fields, Potential Functions, Green’s Theorem, Surface Integrals, Stokes Theorem, Divergence Theorem

Author: Robert Bartle, Donald Sherbert

School: Nnamdi Azikiwe University

Department: Science and Technology

Course Code: MAT251

Topics: real analysis, sets, functions, mathematical induction, finite sets, infinite sets, real numbers, absolute value, real line, intervals, sequences, series, limit theorems, monotone sequences, Cauchy criterion, limits, limit theorems, continuous functions, uniform continuity, inverse function, monotone functions, derivative, mean value theorem, L' Hospital rule, Taylor's theorem, Riemann integral, Riemann integral functions, fundamental theorem, Darboux integral, approximate integrations, pointwise convergence, uniform convergence, exponential functions, logarithmic function, trigonometric functions, infinite series, absolute convergence, infinite integrals, convergence theorems, continuous functions, metric spaces

### Tests related to PROBABILITY 4

School: WAEC, JAMB & POST UTME

Department:

Course Code: JAMB

Topics: Mathematics, JAMB, Logarithm, standard form, permutation, combination, number system, set, ratio, indices, factorization, inequality