= 1 For Y = aX+b, find the relationship between py and px: Suppose that u ~ Unif (-1/2,7/2). Show that x = btan u +c, b>

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1 For Y Ax B Find The Relationship Between Py And Px Suppose That U Unif 1 2 7 2 Show That X Btan U C B 1 (84.2 KiB) Viewed 43 times

= 1 For Y = aX+b, find the relationship between py and px: Suppose that u ~ Unif (-1/2,7/2). Show that x = btan u +c, b> 0 has the Cauchy pdf p(x) = = (1+(***)") ) #0: In importance sampling, suppose you can only compute õ(2) where P(z) = mõ(z) and M is unknown. Show that by replacing ū(z) with õ(z)/9(2), we can still perform importance sampling with the same weights (5.3). Let p(x) = Unif (0, 1) and g(x) = Unif (0,1/2). Let f(x) = x2. Is it true that E, [(4/2ļa)] = Ep[f(x)]? f)p(x 9() = = =