Question

Q4: Suppose X1,X2,...,Xn follows Bernoulli(p), and Y1,Y2,...,Ym follows Bernoulli(p + q), where both 0 < p,q < 0.5. Compute the moment estimator of p and q using first moments.

Answer 1

Solution :-

Given data:-

X 1, X 2,...,X n follows the Bernoulli (p),

Y 1, Y 2,...,Y m follows the  Bernoulli (p +q)

where both are in the condition is 0 < p,q < 0.5

Now, we have to find out the :-

Compute the moment estimator of p and q using first moments :-

The moment estimator of P using first moments. is:-

We know, the first moment of p is,  E(X) = P

    p =

The moment estimator of P is,   =

The moment estimator of q using first moments. is:-

We know, the first moment of q is,  E(Y) = P+q

p+q =

The moment estimator of q  is,  p+q =

  q = -  p

  We know, p =  , then q =   -   

The moment estimator of    is, q =   -