Question Number 148864 by jlewis last updated on 31/Jul/21

A random variable K has a pdf f(k)={_(0 , otherwise) ^e^(−k , 0>k) find E(K) and the cdf

Answered by Olaf_Thorendsen last updated on 01/Aug/21

I suppose f(k) = e^(−k) if k>0 otherwise f is not a pdf. ∫_(−∞) ^(+∞) f(x)dx = ∫_0 ^(+∞) e^(−x) dx = 1 E(K) = ∫_0 ^(+∞) xe^(−x) dx = [x(−e^(−x) )]_0 ^(+∞) − ∫_0 ^(+∞) (−e^(−x) )dx = 1 E(K) =1 F(k) = ∫_0 ^k e^(−x) dx = 1−e^(−k) F(k) = { ((0 if k < 0)),((1−e^(−k) if k ≥ 0)) :}

Commented byjlewis last updated on 01/Aug/21

hello sir,from [x(−e^(−x) )]_0 ^(+∞) I dont get where x has gone, and is x a variable?

Commented byOlaf_Thorendsen last updated on 01/Aug/21

I noted the variable x, but you can write instead of x : z, flower, Mickey or Donald Trump sir, if you prefer.