Question

1. (10 pts) If A and B are independent events (both with probability greater than 0) then which of the following statements must be true?

A. P(A) + P(B) = 1

B. P(A and B) = P(A)P(B)

C. P(A and B) = 0

D. P(A and B) = P(A) + P(B)

2. (10 pts)A salesperson makes “cold calls” trying to sell a product by phone and is successful on each call with probability 1/50. Whether or not he is successful is independent of one call to the next. If he calls 50 people, the number of successful calls are:

A. exactly 1, since he called 50 people and the probability of success is 1/50 each time.

B. at most 1, because once he has been successful he can’t be successful again in the 50 calls.

C. a binomial random variable.

D. equally likely to be 0, 1, or 2.

3. (10 pts) The expected value of a continuous random variable is

A. always computed as n*p.

B. the value that has the highest probability of occurring.

C. always one of the possible values for the random variable.

D. the mean value over an infinite number of observations of the variable

4. (10 pts) You buy coffee at a cafe bene at random times. The following table gives

the probability distribution for X = number of customers in line when you show up

(not including you): k 0 1 2 3 4， P(X=k) 0.15 0.2 0.4 0.2 0.05

What is the probability that there will be at least two people in line when you show up?

A. 0.25

B. 0.40

C. 0.65

D. 0.75

NEED HELP！ THANKS

Answer 1