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1. If X is a hypergeometric random variable with parameters n, K, and N, and p = K/N, the mean
and variance of X are:
a. np and np(1 – p)
b. p and np(1 – p)
c. np and p(1 – p)
d. np and np(1 – p)[(N – n)/(N – 1)]
2. If X is a discrete uniform random variable defined on the consecutive integers 10, 11, …, 20,
the mean of X is:
a. 30
b. 15
c. 12
d. none
3. If S is the sample space of a random experiment and E is any event, the axioms of probability
are
a. P(S) = 1
b. 0 <= P(E) <= 1
c. For any two events E1, E2 with E1 intersect E2 = null, P(E1 union E2) = P(E1) + P(E2)
d. none of the above
e. all of the above
4. Two events A and B are independent with P(A) = P(B) = 0.5. Then P(A intersect B) is:
a. 0.50
b. 0.75
c. 1.0
d. 0.25
5. If X is a binomial random variable with n = 20 and p = 0.25, the mean of X is
a. 10
b. 5
c. 4
d. None
Solution
1. d 2. b (20-10)/2 = 15 3. d 4. d (.5)(.5) =.25 5. b n*p=20*.25=5

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1. If X is a hypergeometric random variable with parameters n, K, an.pdf

  • 1. 1. If X is a hypergeometric random variable with parameters n, K, and N, and p = K/N, the mean and variance of X are: a. np and np(1 – p) b. p and np(1 – p) c. np and p(1 – p) d. np and np(1 – p)[(N – n)/(N – 1)] 2. If X is a discrete uniform random variable defined on the consecutive integers 10, 11, …, 20, the mean of X is: a. 30 b. 15 c. 12 d. none 3. If S is the sample space of a random experiment and E is any event, the axioms of probability are a. P(S) = 1 b. 0 <= P(E) <= 1 c. For any two events E1, E2 with E1 intersect E2 = null, P(E1 union E2) = P(E1) + P(E2) d. none of the above e. all of the above 4. Two events A and B are independent with P(A) = P(B) = 0.5. Then P(A intersect B) is: a. 0.50 b. 0.75 c. 1.0 d. 0.25 5. If X is a binomial random variable with n = 20 and p = 0.25, the mean of X is a. 10
  • 2. b. 5 c. 4 d. None Solution 1. d 2. b (20-10)/2 = 15 3. d 4. d (.5)(.5) =.25 5. b n*p=20*.25=5