Question : = = Suppose Y and X are independent binary random variables, with P(X = 1) = p, P(X = 1) = 1 – p, P(Y= 1) = q
Posted: Wed May 11, 2022 8:20 pm
- Question Suppose Y And X Are Independent Binary Random Variables With P X 1 P P X 1 1 P P Y 1 Q 1 (78.67 KiB) Viewed 26 times
)Question : = = Suppose Y and X are independent binary random variables, with P(X = 1) = p, P(X = 1) = 1 – p, P(Y= 1) = q and P(Y=0)=1 – q. Let Z= X+Y. = ( ) What is the probability mass function (pmf) of Z, p(z) = P(Z = z)? = = ( ) Derive E(Z) and V(Z) ( ) Derive the P(Z = z[X = x)? = ( ) Using the your results in (b), propose a method of moment estimator for p and q. ( ) Now assume that p=q, using the method of maximum likelihood, find an estimator for p.