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Let X and Y be two continuous random variables, Find E(X+Y)*E(X)+E(Y)E(X)-E(Y)E(X)E(Y)E(X)/E(Y)

Question

Let X and Y be two continuous random variables, Find

E(X+Y)∗E(X)+E(Y)E(X)−E(Y)E(X)E(Y)E(X)E(Y) E(X+Y) * E(X) + E(Y) E(X) - \frac{E(Y) E(X) E(Y) E(X)}{E(Y)}

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Solution

The expression you provided seems to be a mathematical one, involving the expected values (E) of two random variables X and Y. Let's simplify it step by step:

  1. E(X+Y)*E(X)+E(Y)E(X)-E(Y)E(X)E(Y)E(X)/E(Y)

First, let's distribute E(X) in the first part of the expression:

  1. E(X)*E(X) + E(Y)*E(X) + E(Y)E(X) - E(Y)E(X)E(Y)E(X)/E(Y)

Then, simplify the expression by combining like terms:

  1. 2*E(X)*E(Y) + E(X)^2 - E(Y)E(X)E(Y)E(X)/E(Y)

Finally, simplify the last term by cancelling out E(Y) from the numerator and denominator:

  1. 2*E(X)*E(Y) + E(X)^2 - E(X)^2

So, the simplified expression is:

  1. 2*E(X)*E(Y)

This is the final simplified form of the given expression.

This problem has been solved

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