here the family of
distribution is normal and it's parameter mu and sigma r
mentioned.
Problem 10: Suppose the yi h, μ are independent random variables with density function where φ > 0 is a fixed constant. Further suppose that μ has marginal density f(μ μ0 Pn) ( 0.5 (27) 0.5 exp(-...
Problem 8: Suppose the Ý, , , Y, β are independent and identically distributed random variables in the interval (0,1) with individual densities where β 〉 0. Further suppose that β has marginal density f(β) 482 exp(-2β). Derive f(B|Y, Y). Identify the distributional family for B and describe its parameters.
Problem 8: Suppose the Ý, , , Y, β are independent and identically distributed random variables in the interval (0,1) with individual densities where β 〉 0. Further suppose that...
(2) Suppose the random variables Yi and Yg have joint probability density function (n 2)-10 The marginal distributions are fi (y) = y/2 for 0 yIS 2 (zero otherwise) and fn (Y2)-2-2y2 for 0 Y2 1 (zero otherwise). (a) Calculate E(Y) and E(Y2) (b) Calculate the conditional densities of YilY2-/2 and Y2Y- (c) Derive ElYalyǐ-m] and EMM-Y21 (d) Calculate EIE(Y1Yİ)] and E [E(YĪ½j. and confirm your answers in (a). (e) Calculate E(YiYo) and compare it with E(Y)E(5).
(2) Suppose the...