Probability generating function when x is even

[chwala]

Homework Statement

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A random variable x has a probability function $G(t)$. Show that the probability that $x$ takes an even value is $\frac 1 2 ( 1+G(-1))$

Homework Equations

The Attempt at a Solution

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$G(t)= \sum_{k=0}^\infty p_k t^k$...
$1=P(X=even)+ P(X=odd)$...1
$G(-1)= (P=even)- P(X=odd)$...2
On solving 1 and 2,
$G(-1)= 2P(X=e) - 1$
→$P(X=e) = \frac 1 2 (1+G(-1))$
guess i was just tired...problem solved.

 

[fresh_42]

Thanks for posting the solution.