Probability Distributions Overview Questions and Answers (100% Correct Answers) Already Graded A

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Probability Distributions Overview
Questions and Answers (100%
Correct Answers) Already Graded A+


Binomial Distribution PMF Ans: P(X = k) = (n choose k) p^k (1 -
p)^(n - k) Where n = number of trials, p = probability of
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success, k = number of successes.


Binomial Distribution Mean Ans: E[X] = np
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Binomial Distribution Variance Ans: Var[X] = np(1 - p)


Geometric Distribution PMF Ans: P(X = k) = (1 - p)^(k - 1) * p
Where p = probability of success, k = trial number of the first
success.


Geometric Distribution Mean Ans: E[X] = 1/p


Geometric Distribution Variance Ans: Var[X] = (1 - p)/p^2


Negative Binomial Distribution PMF Ans: P(X = k) = (k - 1
choose r - 1) p^r (1 - p)^(k - r) Where r = number of successes,
p = probability of success, k = number of trials.


Negative Binomial Distribution Mean Ans: E[X] = r/p


Negative Binomial Distribution Variance Ans: Var[X] = r(1 -
p)/p^2