AAKA
Newbie level 1
Hi, I have a question & I hope to help me.
the Question is:
Every year, a car manufacturer produces X cars, where X is a random variable with probability mass function:
Pr[X=k]=(A/(k+1))p^k , k≥0
Given the number of cars produced, let the amount of profit engine, Y, the car manufacturer makes be a random variable with a pdf:
ƒY(y│X=k)= B*y^k, 0≤y≤1, k≥1
or
ƒY(y│X=k)= δ
, k=0
or
ƒY(y│X=k)= 0 , otherwise
in thousand dollars. Notice that Y is a mixed random variable and Pr(Y=0│X=0)=1, i.e., if the manufacturer does not sell any engines he makes no profit:
(a) Evaluate the constants A and B.
(b) Write down an expression for the unconditional distribution, ƒYin terms of ƒY(y│X=k)and Pr(X=k).
(c) Find the conditional pmf Pr(X=k│Y=k).
(d) Find the conditional pdf, ƒZ(z│X=k),of the total profit,Z=XY, given X=k.
I with if you answer this queston as fast as possible and I will appreciate that.
Yours Truely
Anwar Al-Asam
the Question is:
Every year, a car manufacturer produces X cars, where X is a random variable with probability mass function:
Pr[X=k]=(A/(k+1))p^k , k≥0
Given the number of cars produced, let the amount of profit engine, Y, the car manufacturer makes be a random variable with a pdf:
ƒY(y│X=k)= B*y^k, 0≤y≤1, k≥1
or
ƒY(y│X=k)= δ
, k=0 or
ƒY(y│X=k)= 0 , otherwise
in thousand dollars. Notice that Y is a mixed random variable and Pr(Y=0│X=0)=1, i.e., if the manufacturer does not sell any engines he makes no profit:
(a) Evaluate the constants A and B.
(b) Write down an expression for the unconditional distribution, ƒY
in terms of ƒY(y│X=k)and Pr(X=k). (c) Find the conditional pmf Pr(X=k│Y=k).
(d) Find the conditional pdf, ƒZ(z│X=k),of the total profit,Z=XY, given X=k.
I with if you answer this queston as fast as possible and I will appreciate that.
Yours Truely
Anwar Al-Asam