Let X and Y be independent continuous random variables with respective hazard rate functions X(t) and Y(t), and set W min(X,Y) (a) Determine the distribution function of W in terms of those of X and Y (b) Show that W(t), the hazard rate function of W, is given by W(t) X(t) Y(t) ...

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Let X and Y be independent continuous random variables with respective hazard rate functions X(t) and Y(t),

Question:

Let X and Y be independent continuous random variables with respective hazard rate functions λX(t) and λY(t), and set W = min(X,Y).
(a) Determine the function of W in terms of those of X and Y.
(b) Show that λW(t), the hazard rate function of W, is given by λW(t) = λX(t) + λY(t) Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...