Let X be the random variable with the probability distribution function fx-e-44xx-x-0-1-2-3- then the standard deviation of X is

The correct option is C 2 The above distribution is Poisson Distribution of type nbsp; P(k)=e^ λ.λ^kk! Here λ=4 .Now Mean=Variance=λ in a ...

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Standard XII

Mathematics

Method of Intervals

Let X be the ...

Question

Let X be the random variable with the probability distribution function $f (x) = \frac{e^{- 4} 4^{x}}{x!}; x = 0, 1, 2, 3, . . . .$ then the standard deviation of X is

2

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4

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16

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\sqrt{2}

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Solution

The correct option is C $2$
The above distribution is Poisson Distribution of type
$P (k) = \frac{e^{- λ} . λ^{k}}{k!}$
Here $λ = 4$ .
Now $M e a n = V a r i a n c e = λ$ in a Poisson Distribution.
Hence
$V a r i a n c e = λ = 4$
Or
$S . D^{2} = V a r i a n c e = 4$
Or
$S . D = \sqrt{V a r i a n c e} = \sqrt{4}$
$= 2$ .

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Let X be the random variable with the probability distribution function f(x)=e−44xx!;x=0,1,2,3,.... then the standard deviation of X is

The correct option is C 2The above distribution is Poisson Distribution of type P(k)=e−λ.λkk!Here λ=4.Now Mean=Variance=λ in a Poisson Distribution.HenceVariance=λ=4Or S.D2=Variance=4Or S.D=√Variance=√4=2.

Let X be the random variable with the probability distribution function $f (x) = \frac{e^{- 4} 4^{x}}{x!}; x = 0, 1, 2, 3, . . . .$ then the standard deviation of X is