Maharashtra State BoardHSC Commerce 12th Board Exam
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Solve the following problem : If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, find variance of X. - Mathematics and Statistics

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Sum

Solve the following problem :

If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, find variance of X.

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Solution

Given, P[X = 1] = 0.4, P[X = 2] = 0.2,
e–1 = 0.3678
For Poisson distribution,
X ~ P(m)
The p.m.f. of X is given by

P[X = x] = `("e"^(-"m")"m"^x)/(x!)`

Now,
P[X = 1] = `("e"^(-"m")"m"^1)/(1!)` = me-m

∴ 0.4 = me-m               ...(i)

P[X = 2] = `("e"^(-"m")"m"^2)/(2!)` = `("m"^2"e"^(-"m"))/(2)`

∴ 0.2 = `("m"^2"e"^(-"m"))/(2)`

∴ 0.4 = m2 e–m          ...(ii)

∴ `(0.4)/(0.4) = ("m"^2"e"^(-"m"))/("me"^(-"m"))`     ...[From (i) and (ii)]

∴ m=1
∴ X ~ P(1)
∴ Var (X) = m = 1.

Concept: Poisson Distribution
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.13 | Page 157

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