# find probability based on Joint Density Function

Looking to see how the answer is derived.

Suppose that X and Y are independent each with exponential distribution with parameter = 3. Joint Density Function = 9(e^-3x)x(e^-3y) for x>0 and y>0.

Find (a) P(X + 2Y <,= 2);

(b) P(X + Y <,= 2); and

(c) P(X - Y <,= 2).

<,= represents less than, equal to.

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#### Solution Preview

Hi there,

I've attached my answer in the word document.

P(x+2y<=2)=∫_0^2▒∫_0^(1-x/2)▒〖(9e^(-3x) 〗 ...

#### Solution Summary

The solution provides detailed explanations how to find out the probability based on Joint Density Function.

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