Description of Probability distribution function

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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