The answer .8414 was found to be incorrect
Here we need to use very large value of n ( sample size). Because geometric distribution is highly positively skewed.
So for verylarge n,we can use centrallimit theorem.
The answer .8414 was found to be incorrect Fori 2 1, let X G1/2 be distributed...
Fori 2 1, let XiG1/2 be distributed Geometrically with parameter 1/2. Define Vn. i-1 Approximate P-1 Yn < 2) with large enough n Hint, note that Yn is not "properly" normalized
Fori 2 1, let X G1/2 be distributed Geometrically with parameter 1/2. Ai G/ be distributed Geometrically with parameter Define Vn i=1 Approximate P-1 Zn S2) with large enough n Hint, note that Zn is not "properly" normalized.
For i 1, let X G1/2 be distributed Geometrically with parameter 1/2 Define Xi -2 Approximate P (-1 < -2) with large enough n.
Exercise 6.14 Let y be distributed Bernoulli P(y = 1) unknown 0<p<1 p and P(y = 0) = 1-p f or Some (a) Show that p E( (b) Write down the natural moment estimator p of . (c) Find var (p) (d) Find the asymptotic distribution of vn (-p) as no. as n> OO.
Problem 2: Let X be a binomially distributed random variable based on n 10 trials with success probability p 0.3. a) Compute P(X 3 8), P(x-7 and PX> 6) by hand, showing your work.
8. Let X1...., X, be i.i.d. ~E(1) random variables (i.e., they are independent and identically distributed, all with the exponential distribution of parameter 1 = 1). a) Compute the cdf of Yn = min(X1,...,xn). b) How do P({Y, St}) and P({X1 <t}) compare when n is large and t is such that t<? c) Compute the odf of Zn = max(X1...., X.). d) How do P({Zn2 t}) and P({X1 2 t}) compare when n is large and t is such...
Problem 41.3 Let X and Y be independent random variables each geometrically distributed with parameter p, i.e. p(1- p otherwise. Find the probability mass function of X +Y
1. Suppose that X, X, X, are iid Berwulli(p),0 <p<1. Let U. - x Show that, U, can be approximated by the N (np, np(1-P) distribution, for large n and fixed <p<1. 2. Suppose that X1, X3, X. are iid N ( 0°). Where and a both assumed to be unknown. Let @ -( a). Find jointly sufficient statistics for .
Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 = X(1), and Yk = X(k) – X(k-1), 2<k<n. Find the joint pdf of Yı,Y2, ...,Yn. Hint: Note that (Y1,Y2, ...,Yn) = g(X(1), X(2), ..., X(n)), where g is invertible and differentiable. Use the change of variable formula to derive the joint pdf of Y1, Y2, ...,Yn.
CPoisson can not be determined. distribution P(np) ) Suppose X~N(0,1) and YN(24), they are independent, then (is incorrect. DX+Y-N(2, 5) BP(Y <2)>0.5 -Y-N (-2,5) D Var(X) < Var(Y) 5) Suppose X,Xy..,X, (n>1) is a random sample from N(μ,02) , let-ly, is| then Var(x)- ( Instruction: The followins ass