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CDF of product of two *translated* exponential variables

CDF of product of two *translated* exponential variables
  1. How do you find the CDF of two random variables?
  2. How to find expected value of two random variables multiplied?

How do you find the CDF of two random variables?

To find the joint CDF for x>0 and y>0, we need to integrate the joint PDF: FXY(x,y)=∫y−∞∫x−∞fXY(u,v)dudv=∫y0∫x0fXY(u,v)dudv=∫min(y,1)0∫min(x,1)0(u+32v2)dudv.

How to find expected value of two random variables multiplied?

In general, the expected value of the product of two random variables need not be equal to the product of their expectations. However, this holds when the random variables are independent: Theorem 5 For any two independent random variables, X1 and X2, E[X1 · X2] = E[X1] · E[X2]. E[Xi].

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