6. Let X N (100, 25). Find the following: (a) P(X < 100) Answer: 1/2, (b)...
8. Let X (i-1,2) be independent N(0,1) random variables. a. Find the value of c such that P ( (X1 + X2 )2/( X2 -X1)2 < c ) =.90 b. Find P(2 X1 -3 X2< 1.5) c. Find 95th percentile of the distribution of Y-2 X1 -3 X2
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 .
Suppose that NoP(X5)6 and P(X 2):2 find P( 3< X < 4).
8. Let X.(i-12) be independent N(0,1) random variables. a. Find the value of c such that P ( (X1 + X2尸/( X2-X)2 < c ) =.90 b. Find P(2 X1 -3 X21.5) c. Find 95th percentile of the distribution of Y-2X -3X2
6. Let X have a N(1,2) distribution. Using only the tables, find: a) P(X 1.5) b) P(-1.1 X < 3.3) c) P(X-.9) d) A point c such that P(X > c) = 01 e) A point d such that P(X < d) 005
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.
6. Let f(x,y) = 1 if 0 < y < 2x, 0<x<1, and 0 otherwise. Find the following: a) f(y|x) b) E(Y|X = x) c) The correlation coefficient, p, between X and Y
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
(a) Find P{X=2}
(b) Find P{X<2}
(c) Find P{2 <= X < 2.5}
The cumulative distribution of a random variable X is given as 0 x < 0 0<x<2 4 Fx(x) = 2<x<3 4 x 3 x + 1