If two random variable X and Y are connected by relation 2 X -3 Y 5 X +4 Y =4 and X follows Binomial distribution with parameters n=10 and p= 1 2 , then what is the variance of Y ?

Step-by-step solution

2 x-3 y 5 x+4 y =4 aligned & 2 x-3 y=20 x+16 y & 19 y=18 x & y= 18 x 19 & var .(x)=n p q=n p(1-p) & =10 1 2 1 2 = 5 2 & Now, var. (y)= var . (- 18 19 x ) & var. (y)= ( 18 19 )^2 5 2 = 810 361 aligned