probability

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 .

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]=

  1. 👍 3
  2. 👎 1
  3. 👁 2,250
  1. 1:
    1/2400
    0

    2:
    2/3

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

    4:
    no answer

    5/7 result

    1. 👍 5
    2. 👎 1
  2. 3.
    c. 0

    4. 40/3

    1. 👍 5
    2. 👎 1
  3. 3.
    b) (-z/4800)+(1/60)

    1. 👍 4
    2. 👎 1

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