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

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SUMMARY

The expected value of the maximum of two independent geometric random variables, X and Y, with probabilities of success p and q respectively, can be calculated using order statistics. The probability density function f(y) and the cumulative distribution function F(y) are essential for determining the maximum's expected value, E(max(X,Y)). The formula Y(n) = n * f(y) * [F(y)]^(n-1) is used to derive the probability of the maximum, followed by integration to find the expected value. Proper definition of the variables' intervals is critical for accurate integration.

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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))
 
Last edited:
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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.
 
Last edited:

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