Question

Please answer all parts of the question. Thank you

[2] X is continuous uniform (1,7) while Y is exponential with mean 2. If the variance of (X+2Y) is 20, find the correlation coefficient of X and Y.

Answer 1

hire a Ru - Xy continuous u uniform the interval (1,7) le .xnulla) and we know that if xuuca, b) then W(x) = (b-a) 2 12 sinll Here xnuc, then vex) = (7-1)? -(-2 32 lux) :3

and y is exponental with mean2 il yui exp(mean:") we know that if yu exflmeanse then (x) = 2 Hire. since. Here xu exp (mean 2) solved to lux v(x)= 2²= 22 Further Here it is give that 0( x + 1) 20 u(x) + 4V(7) - 2.9. An (x,y) = 20 3+ 4x4 - 4.Qulx,1):2

3+16 - 4 GN (x,y) = 20 19 - 4 aw (4,0 220 -4 au (x4) 20-19:) ciu (x+4) -0.25 a Nind we know the correlation between x and y au(x,y) -0.25 f FTVG 7374 le R 0.7217