Sophia is vacationing in Monte Carlo. On any given night, she takes X dollars to the casino and returns with Y dollars. The random variable X has the PDF shown in the figure. Conditional on X=x , the continuous random variable Y is uniformly distributed between zero and 3x .

Question

1. Find the PDF of Z . Express your answers in terms of z using standard notation.

If −40<z<0 :
fZ(z)=

If 0<z<80 :
fZ(z)=

If z<−40 or z>80 :
fZ(z)=

2. What is E[Z] ?

E[Z]=

Answer 1

1:
1/2400
0

2:
2/3

3:
(40+z)/2400
no answer
0

4:
no answer

5/7 result

Answer 2

3.
c. 0

4. 40/3

Answer 3

3.
b) (-z/4800)+(1/60)

Answer 4

1. 1/2400, 0
2. 2/3
3. (40+z)/2400, (-z/4800)+(1/60), 0
4. 40/3