Leiter and Hamdan (1973) model traffic accidents and fatalities at a specific location in a given time

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Leiter and Hamdan (1973) model traffic accidents and fatalities at a specific location in a given time interval. They suppose that the number of accidents X has a Poisson distribution with parameter λ. If X = x, then the number of fatalities Y has a binomial distribution with parameter p.

(a) Find the marginal distribution of the number of fatalities.
(b) Show that the conditional distribution of X given Y = y is a Poisson distribution with parameter λ(1 − p), which has been “shifted” y units to the right.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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