Q5 (please also show the steps):
CLT = Central Limit Theorem
Solution,
(1)
and
and
Therefore,
is an unbiased estimator of p1 - p2.
mean square error is given by-
{ samples and independent and mean deviantion about mean is 0}
(2)
Central limit theorem states that if we have population with
mean
and standard deviation
if we take sufficiently large random samples the distribution of
samples mean will be approximately distributed as
,
and normally distribution
Hence, proved that
Q5 (please also show the steps): CLT = Central Limit Theorem Q5 Consider a problem of estimating...
Q5 Consider a problem of estimating the difference of proportions for two populations. In sample 1, out of nį subjects, Si of them are “successes” and the rest are “failures”. In sample 2, out of n2 subjects, S2 of them are “successes” and the rest are "failures”. It is known that Si ~ B(n1, p1) and S2 ~ B(n2, P2). We are interested in estimating p1 – P2. Si and 2 1. Denote ſi S. Show that Ôi – P2...
1. Suppose YPoisson(A) and Y2 ~Poisson(2X) are two independent observations. (a) Derive the MLE of λ based on (Yi,Yo) (b) Show that the estimator λ (Y + Y)/3 is unbiased for λ and compute its variance. (c) With as much rigor as possible, show that if A is large then (A-X)/v is approximately normally distributed. (d) Derive a 95 percent confidence interval for A based on the asymptotic distribution of λ in part (c) (e) Extra Credit Based on part...