- #1
Gregg
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The discrete random variable X has probability density P(X=x) =kp^x for x=0,1,... where p \in (0,1). Find normalizing constant k and E(X) as functions of p. For each integer x>0 find P(X>=x) and hence find P(X=y|X>=x) for each integer y>0.
found k=1-p
[tex] E(X)=\sum kxp^x =p/(1-p)[/tex]
[tex]P(X>=x) = 1-\sum_{x'=0}^{x} kp^x' = p^{x+1}[/tex]
P(X=y|X>=x) =?
found k=1-p
[tex] E(X)=\sum kxp^x =p/(1-p)[/tex]
[tex]P(X>=x) = 1-\sum_{x'=0}^{x} kp^x' = p^{x+1}[/tex]
P(X=y|X>=x) =?