Question

Remember to round all answers to the second decimal point

QUESTION 1

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either1, 2, 3, 4 or 5. 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. Use this information to answer the following questions.

f(x) =   for x= 1, 2, 3, 4 and 5

Compute P(x = 2).

QUESTION 2

Compute P(x ? 3).

QUESTION 3

Compute P(x > 3).

QUESTION 4

Compute the expected value of this distribution.

Answer 1

1)

P(X=2) =2/15

2)

P(X<=3)=P(X=1)+P(X=2)+P(X=3)=1/15+2/15+3/15=6/15=2/5

3)

P(X>3) =1-P(X<=3)=1-2/5=3/5

4)

expected value = $\sum$ xP(x)=1*(1/15)+2*(2/15)+3*(3/15)+4*(4/15)+5*(5/15)=55/15=11/3