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.© BrainMass Inc. brainmass.com October 2, 2020, 2:59 am ad1c9bdddf
I've attached my answer in the word document.
P(x+2y<=2)=∫_0^2▒∫_0^(1-x/2)▒〖(9e^(-3x) 〗 ...
The solution provides detailed explanations how to find out the probability based on Joint Density Function.