- Question 14 A A Density Function Sometimes Used To Model Lengths Of Life Of Electronic Components Is The Rayleigh Den 1 (148.58 KiB) Viewed 23 times
)Question 14: (a) A density function sometimes used to model lengths of life of electronic components is the Rayleigh density which is given by: if x > 0 f (x|0) = = { *exp(-5) otherwise. If X has a Rayleigh density, find the p.d.f. of U = X2. (b) Suppose that the opening prices per share of two similar stocks, X1 and X2, are inde- pendent random variables each with density function: = $ (zlo) = { (1) exp(-) if = 24 otherwise. On a given morning an investor is going to buy shares in whichever stock is less ex- pensive. Find the probability density function for the price per share that the investor will have to pay. (c) The Weibull probability density function is given by Imxm-1 exp(-) if x > 0 0 otherwise. f(z|6, m) = { = If X has a Weibull density find the probability density function of U = X". [This is a generalization of the problem in part (a), which has m = 2.]