STAT 330 - CHAPTER 5 | GUARANTEED SUCCESS STARTS
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What is the Bernoulli distribution? Answer: A distribution with two outcomes: success (p) or
failure (1-p).
Q: What is the mean of a Bernoulli random variable? Answer: μ = p.
Q: What is the variance of a Bernoulli random variable? Answer: σ² = p(1-p).
Q: What is the binomial distribution? Answer: The distribution of the number of successes in n
independent Bernoulli trials with success probability p.
Q: What is the pmf of a binomial distribution? Answer: P(X=k) = C(n,k) p^k (1-p)^(n-k).
Q: What is the mean of a binomial distribution? Answer: μ = np.
Q: What is the variance of a binomial distribution? Answer: σ² = np(1-p).
Q: What is the geometric distribution? Answer: The distribution of the number of trials until the
first success.
Q: What is the pmf of the geometric distribution? Answer: P(X=k) = (1-p)^(k-1)p, k=1,2,...
Q: What is the mean of a geometric distribution? Answer: μ = 1/p.
Q: What is the variance of a geometric distribution? Answer: σ² = (1-p)/p².
Q: What is the negative binomial distribution? Answer: The distribution of the number of trials
until the rth success.
Q: What is the pmf of the negative binomial distribution? Answer: P(X=k) = C(k-1, r-1) p^r (1-
p)^(k-r), k=r,r+1,...
Q: What is the mean of a negative binomial distribution? Answer: μ = r/p.
Q: What is the variance of a negative binomial distribution? Answer: σ² = r(1-p)/p².
Q: What is the hypergeometric distribution? Answer: Models number of successes in n draws
without replacement from population of size N with M successes.
Q: What is the pmf of the hypergeometric distribution? Answer: P(X=k) = [C(M,k) C(N-M, n-k)] /
C(N,n).
Q: What is the mean of a hypergeometric distribution? Answer: μ = n(M/N).
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HERE! LEARN, PRACTICE & EXCEL!
What is the Bernoulli distribution? Answer: A distribution with two outcomes: success (p) or
failure (1-p).
Q: What is the mean of a Bernoulli random variable? Answer: μ = p.
Q: What is the variance of a Bernoulli random variable? Answer: σ² = p(1-p).
Q: What is the binomial distribution? Answer: The distribution of the number of successes in n
independent Bernoulli trials with success probability p.
Q: What is the pmf of a binomial distribution? Answer: P(X=k) = C(n,k) p^k (1-p)^(n-k).
Q: What is the mean of a binomial distribution? Answer: μ = np.
Q: What is the variance of a binomial distribution? Answer: σ² = np(1-p).
Q: What is the geometric distribution? Answer: The distribution of the number of trials until the
first success.
Q: What is the pmf of the geometric distribution? Answer: P(X=k) = (1-p)^(k-1)p, k=1,2,...
Q: What is the mean of a geometric distribution? Answer: μ = 1/p.
Q: What is the variance of a geometric distribution? Answer: σ² = (1-p)/p².
Q: What is the negative binomial distribution? Answer: The distribution of the number of trials
until the rth success.
Q: What is the pmf of the negative binomial distribution? Answer: P(X=k) = C(k-1, r-1) p^r (1-
p)^(k-r), k=r,r+1,...
Q: What is the mean of a negative binomial distribution? Answer: μ = r/p.
Q: What is the variance of a negative binomial distribution? Answer: σ² = r(1-p)/p².
Q: What is the hypergeometric distribution? Answer: Models number of successes in n draws
without replacement from population of size N with M successes.
Q: What is the pmf of the hypergeometric distribution? Answer: P(X=k) = [C(M,k) C(N-M, n-k)] /
C(N,n).
Q: What is the mean of a hypergeometric distribution? Answer: μ = n(M/N).
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