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प्रश्न
If X~P(0.5), then find P(X = 3) given e−0.5 = 0.6065.
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उत्तर
Given, X ~ P(0.5) and e–0.5 = 0.6065
∴ m = 0.5
The p.m.f. of X is given by
P(X = x) = `("e"^-"m""m"^x)/(x!)`
∴ P(X = x) = `("e"^(-0.5) (0.5)^x)/(x!), x` = 0, 1, 2,...
∴ P(X = 3) = `("e"^(-0.5) (0.5)^3)/(3!)`
= `(0.6065 xx 0.125)/(3 xx 2 xx 1)`
= 0.0126
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∴ P(X = 1) = `square` P(X = 2).
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∴ m = `square`
State whether the following statement is true or false:
lf X ∼ P(m) with P(X = 1) = P(X = 2) then m = 1.
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Since P[X = 2] = P[X = 3]
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∴ m = `square`
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