Determine whether the distribution shown below is a valid probability distribution.

X	p(x)
21	0.28
28	0.17
34	0.28
40	0.27

(b)What are the only reasonable values ofX?

1.

2.

3.

4.

(Enter your answers from smallest to largest.) , , ,

(c)What is the probability thatX=34?

(d)What is the probability thatX=24?

(e)What is the probability thatXis more than36?

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed.

p(x) = x/6 for x= 1, 2, or 3

(a)Is this probability function valid? Explain.

(b)What is the probability that it takes exactly 2 sessions to gain the patient's trust? (Round your answer to three decimal places.)

(c)What is the probability that it takes exactly 4 sessions to gain the patient's trust? (Round your answer to three decimal places.)

(d)What is the probability that it takes at least 2 sessions to gain the patient's trust? (Round your answer to three decimal places.)

(e)What is the probability that it takes at most 2 sessions to gain the patient's trust? (Round your answer to three decimal places.)

Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S).

The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed.

List five different outcomes and their associatedy-values.

Outcome	Value ofy
RS
RLS
S
LS
LRRLS