# 1. Suppose that the number of red blood corpuscles in humans, denotedby X, follows a Poisson distribution whose parameter depends on theobserved individual. For a person selected at random we may considerthe parameter value Y as anthat Y y, we have XExp(a) random variable such that, givenPoisson(y); namely,Exp(a)X | Y yPoisson(y), with YHere a is apositive constant and the density function of Exp(a) isf(y)aeay, y > 0(a) Find the conditional expectation E(X|Y = y), where y 0(b) Compute the expectation E(X). Remark: You may use the lawof total expectation.(c) Find the distribution of X. Remark: You may use the law oftotal probability: P(X k) = So P(X k|Y y)fy (y)dy

Question

I need an easy to understand solution with a thorough explanation. I have no good background in probability. I hope you will provide me with a very good solution, Thank you very much

Step 1

Find the condition expectation

Step 2

1.b)

Compute the Expectati...

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