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Statistics Question on Standard Univariate Distributions

Let 𝑋 and π‘Œ be jointly distributed random variables such that, for every fixed πœ†>0, the conditional distribution of 𝑋 given π‘Œ=πœ† is the Poisson distribution with mean πœ†. If the distribution of π‘Œ is πΊπ‘Žπ‘šπ‘šπ‘Ž (2, 12\frac{1}{2} ), then the value of 𝑃(𝑋= 0)+𝑃(𝑋=1) equals

A

727\frac{7}{27}

B

2027\frac{20}{27}

C

827\frac{8}{27}

D

1627\frac{16}{27}

Answer

2027\frac{20}{27}

Explanation

Solution

The correct option is (B): 2027\frac{20}{27}