# How do we calculate the E(max(x,y))

## Main Question or Discussion Point

if we have two Independent geomtrice variables x and y ,
with prob of success for x is p and for y is q
how do we calculate the E(max(x,y))

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First, using order statistics, find the probability of the maximum of x and y.

That is, Y(n) = n * f(y) * [F(y)]^(n-1)

Use the probability density function for f(y), and the cumulative distribution function for F(y) (or just integrate the density function f(y)).

Once you have Y(n), finding its expected value is as simple as applying the definition. Also, make sure your variables are defined on the correct intervals. This will be crucial for integration.

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