A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1. a) Prove that the characteristic function (CF) of the random variable X is Ø, (t) = e²(e¹-1). b) Use the CF in (a) to find the mean and variance of the random variable X.

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QUESTION 4
A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1.
a)
Prove that the characteristic function (CF) of the random variable X is Ø₂(t) = e²(eit-1).
b)
Use the CF in (a) to find the mean and variance of the random variable X.
Transcribed Image Text:QUESTION 4 A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1. a) Prove that the characteristic function (CF) of the random variable X is Ø₂(t) = e²(eit-1). b) Use the CF in (a) to find the mean and variance of the random variable X.
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