Suppose that the random variables (Y, Y2) have a joint probability density function (pdf) of the form f( 172) = ke (ityz) 0 , y1 2 0, yz > O , elsewhere (a) Determine k so that f is indeed a pdf

Statistics Nov 20, 2020

Suppose that the random variables (Y, Y2) have a joint probability density function (pdf) of the form f( 172) = ke (ityz) 0 , y1 2 0, yz > O , elsewhere (a) Determine k so that f is indeed a pdf. (b) Evaluate P(Y, > 1, Yz < 2). (c) Evaluate P(Y1 + Y2 < 3). (d) Find the marginal pdf of Y2. (e) Find the conditional pdf of Y1 , given Y2 = 2. K (f) Are Y, and Y2 independent? Justify. (g) What is the 90th percentile of Y,?