Question Number 148620 by jlewis last updated on 29/Jul/21

consider the following pdf of a random variable X f(x)={Σ_(i=0) ^∞ [(−x^2 )i/i!]_(0 otherwise) ^(x>0) find the variance X

Answered by Olaf_Thorendsen last updated on 29/Jul/21

f(x) = Σ_(i=0) ^∞ (−1)^i (x^(2i) /(i!)) = e^(−x^2 ) ∫_(x>0) f(x)dx = ∫_0 ^(+∞) e^(−x^2 ) dx = ((√π)/2) ≠ 1 This is not a pdf.