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. Determine the joint PDF fX,Y(x,y).

If 0<x<40 and 0<y<3x:

fX,Y(x,y)= ?

If y<0 or y>3x:

fX,Y(x,y)= ?

2. On any particular night, Sophia makes a profit Z=Y−X dollars. Find the probability that Sophia makes a positive profit, that is, find P(Z>0).

P(Z>0)= ?

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

Hint: Start by finding fZ∣X(z∣x).

If −40<z<0:

fZ(z)= ?

If 0<z<80:

fZ(z)= ?

If z<−40 or z>80:

fZ(z)= ?

4. What is E[Z]?

E[Z]= ?

Answer 1

What figure? Cannot copy and paste here.

Answer 2

1.a. 1/2400
1.b. 0
2. 2/3
3.c. 0 (zero)
The others I don't know

Answer 3

Show how prime numbers can be multiplied to equal 27. Help

Answer 4

hi i need help in sience

Answer 5

i like sience better than math

Answer 6

science*