Probability distribution function
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Please give step-by-step process for solving the following probability problems.
Let X ~ Exp(lamda1) and that Y ~ Exp(lambda2).
Further assume that X and Y are independent.
(a) Write down the joint pdf (probability distribution function) of X and Y, fXY(x,y).
(b) For t > 0, prove that P(Y < tX) = t lambda2 / ( lambda1 + t lambda2).
(c) For simplicity, assume that lambda1 = lambda2 = 1, and let T = Y/X.
Use part (b) to find the pdf (probability distribution function) of T, fT(t).
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Probability distribution function is utilized in the solution.
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