Statistics | Poisson Distribution Sample Question | GATE DA

Question

Let $0, 1, 1, 2, 0$ be five observations of a random variable $𝑋$ which follows a Poisson distribution with the parameter $𝜃 > 0$. Let the minimum variance unbiased estimate of $𝑃(𝑋 ≤ 1)$, based on this data, be $𝛼$. Then $5^4𝛼$ (in integer) is equal to _____________

Answer 1

Aswer is 505.

just find the sample mean of the data(It is the mean of the possion distribution)

Then computte the alpha

Then 5^4 * alpha