Question

7. Variance of Poisson Distribution: Let X ~ Pois(?), ? > 0, with p.m.f. p(x) = (?^x * e^-?) / x!, x = 0, 1, 2, ... Show that Var(X) = ?.

          7. Variance of Poisson Distribution: Let X ~ Pois(?), ? > 0, with p.m.f.

p(x) = (?^x * e^-?) / x!, x = 0, 1, 2, ...

Show that Var(X) = ?.

Added by Rebecca Y.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/22/2023

Step 1

First, recall the mean and variance formulas for a Poisson distribution: Mean: E(X) = A Variance: Var(X) = E(X^2) - (E(X))^2 We need to find E(X^2) and then use the variance formula to show that Var(X) = A. Show more…

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Variance of Poisson Distribution: Let X ~ Pois(A); A > 0, with p.m.f. P(X = k) = (e^(-A) * A^k) / k!, where k = 0, 1, 2, ... Show that Var(X) = A.

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Question

7. Variance of Poisson Distribution: Let X ~ Pois(?), ? > 0, with p.m.f. p(x) = (?^x * e^-?) / x!, x = 0, 1, 2, ... Show that Var(X) = ?.

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