Answer all three questions in this section2. Let V and W be two random variables with joint probability density function givenbyfvw (v,w) = aw exp(-dv +(8-A)w²), w>0, v> w²,where A, & are positive constants.(a) Find the value of a.(b) Consider the transformationX = WP, Y=V_W².Find the joint density of X and Y. Hence show that X and Y are independentexponential random variables.(c) State the distribution of AX + SY.

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Answered: where , & are positive constants. (a)…

Calculus For The Life Sciences

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Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

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where , & are positive constants. (a) Find the value of a. (b) Consider the transformation X = WP, Y=V_W². Find the joint density of X and Y. Hence show that X and Y are independent exponential random variables. (c) State the distribution of AX + SY.