A
Anjum
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ii) Consider a pair of random variables X and Y with the following properties: X is a discrete random variable Y is a continuous random variable The unconditional distribution of Y is exponential with parameter λ (> 0) Conditional on Y = y, X follows a Poisson distribution with expected value y. a) Show that the unconditional distribution of X is the distribution described in part (i) for a particular value of p.
Here we have P(X|Y=Y)=(e^-y)*(y^x)\x!
Then to find marginal distribution of x why are integrating the multiplication of conditional density of x given y with marginal density of y
Here we have P(X|Y=Y)=(e^-y)*(y^x)\x!
Then to find marginal distribution of x why are integrating the multiplication of conditional density of x given y with marginal density of y