Question

Question 3 [17 marks] The random variables X and Y are continuous, with joint pdf 0 y otherwise ce fxx (,y) a) Show that cye fr (y) otherwise and hence that c = 1. What is this pdf called? (b) Compute E (Y) and var Y; (c) Show that { > 0 fx (a) e otherwise (d) Are X and Y independent? Give reasons; (e) Show that 1 E(XIY 2 and hence show that E (XY) =.

Answer 1

oMarginal ostriouh'on g i ginn b integnahng oiat pat i upect Ce d fyy2 -y C Cye Sina Lfy D dy dy C (t)J

fyly othuruwise amma2, 1) where shape panamela nat panameta ) ElY)= yyedy dy 2 17 EY)-EY O- 6

Lee dy (7) dy -e e otherewie

L P e wnite t eint pd pnoduct mmginot pdf nnet say that xy Sincu canmol Y a lodipendiat

according to HomeworkLib policy, we are asked to do only the first four questions. Kindly upload the last question again.