Question:

Let 𝑋 and 𝑌 be jointly distributed random variables such that, for every fixed 𝜆>0, the conditional distribution of 𝑋 given 𝑌=𝜆 is the Poisson distribution with mean 𝜆. If the distribution of 𝑌 is 𝐺𝑎𝑚𝑚𝑎 (2, $\frac{1}{2}$ ), then the value of 𝑃(𝑋= 0)+𝑃(𝑋=1) equals

IIT JAM MS - 2023
IIT JAM MS

Updated On: Oct 1, 2024

$\frac{7}{27}$
$\frac{20}{27}$
$\frac{8}{27}$
$\frac{16}{27}$

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The Correct Option is B

Solution and Explanation

The correct option is (B):

\frac{20}{27}

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The Correct Option is B

Solution and Explanation

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