ISYE 2027 Exam Questions and Answers Solved Correctly

ISYE 2027 Exam Questions and Answers Solved Correctly Bernoulli - Answers An event either occurs or does not occur Bernoulli Parameter - Answers P Bernoulli PMF - Answers P if 1, 1-P if 0, 0 otherwise Bernoulli's E[x] - Answers P Bernoulli Variance - Answers p(1-p) Binomial - Answers Number of successes within n trials Binomial Parameters - Answers (n,p) Binomial PMF - Answers (nCk)(p^k)(1-p)^(n-k) Binomial E[x] - Answers np Binomial Variance - Answers np(1-p) Geometric - Answers Keep doing trials until first success Geometric Parameters - Answers P Geometric PDF - Answers 1-(1-p)^k Geometric E[x] - Answers 1/p Geometric Variance - Answers (1-p)/p^2 Poisson Distribution - Answers The likelihood of a particular number of independent events within a particular interval Poisson PMF - Answers ((e^-λ)(λ^x))/x! Poisson E[x] - Answers λ Poisson Variance - Answers λ Which distributions have the memoryless property? - Answers Exponential and Geometric Exponential Parameter - Answers λ Exponential E[x] - Answers 1/λ Exponential Variance - Answers 1/λ^2 Exponential PDF - Answers λe^-x Exponential CDF - Answers 1-e^-λx Uniform Parameters - Answers (a,b) Uniform E[x] - Answers a+b/2 Uniform Variance - Answers (b-a)^2/12 Uniform PDF - Answers 1/(b-a) Uniform CDF - Answers (x-a)/(b-a) y=ax+b E[x] - Answers a*E[x] +b y=ax+b Variance - Answers a^2 * Var(x)