Let X1,...Xn be a random sample from a geometric distribution, X~GEO(p). Find the MLEs of the following quantities: (using the invariance property of the MLE)
a) p;
b)E(X) = 1/p^2;
c) Var(X) = (1-p)/p^2;
d) P[X>8] = (1-p)^8.
Let X1,...Xn be a random sample from a geometric distribution, X~GEO(p). Find the MLEs of the following quantities: (using the invariance property of the MLE)
a) p;
b)E(X) = 1/p^2;
c) Var(X) = (1-p)/p^2;
d) P[X>8] = (1-p)^8.