Let X and Y be independent random variables which are exponential with parameter λ > 0. Then each has a probability density function equal to f(x) = λe^(-λx) when x > 0, and zero otherwise. Compute the probability density function of 2X + 3Y.
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For 2X, we have: f(2X)(x) = P(2X = x) = P(X = x/2) = f(X)(x/2) = A*e^(-x/2) Similarly, for 3Y, we have: f(3Y)(y) = P(3Y = y) = P(Y = y/3) = f(Y)(y/3) = A*e^(-y/3) Now, we need to find the probability density function of 2X + 3Y. Let z = 2X + 3Y. Show more…
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