6. Suppo e () ~ N (C:J& use the formula p(xly) = p(1) ). Find the...
6. Suppose C) ~ N (C), Ģ:: ru). Find the distribution of X|Y. Hint use the formula p p(y) 7. Consider i.i.d. observations Xi, .., Xn ~ N(H, 1) (a) Compute E(XiX). Hint: use the above problem, and find the conditional distribution of Xi given X first (b) Compute E (ix)
9. Let the joint density function of (X, Y) be E (0, oo fa,y) ye e forx (O,co) and y (o, co) (a) [4 points] Find fr) and fxy(xly) (b) [3 points] Compute the conditional expectation E(XIY). (c) [3 points] Find P(X > 3Y 1)
Assume that X~ Bin(n, p) Find the variance of X algebraically. Hint: First find E(X(X-1)) Use M () to find V(X) 1. а. b.
5) Consider the polynomial P() z2-z-1. (a) Find two integers n, m E Z, so that P(x) has a zero in [n, m. (b) Use the bisection method twice to get an approximation to the zero of P(x) in n, m] (c) Use Newton's method twice to get an approximation to the zero of P() in n,m (d) Use the quadratic formula to find the actual zero of P() in [n, m (e) Compute the relative %-error for each of...
1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2. Compute p(X 0) 3. Compute E(X). Hint: use the CDF expectation formula, and integration by parts. You may assume that lim, t"o(-t) 0 for all n 2 0. 4. Find the CDF Fx (u) 5. Compute V(X). Hint: use Fxa, and follow the same hint of part (3)
1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2....
Find a formula for the sum of n terms. Use the formula to find the limit as n →0. n lim n00 -(i – 1)2 i = 1 Free
Problem 6. Let P be an n × n permutation matrix with 1's on the anti-diagonal. Find det(P), Hint: How many exchange permutations are needed to implement P?
Problem 6. Let P be an n × n permutation matrix with 1's on the anti-diagonal. Find det(P), Hint: How many exchange permutations are needed to implement P?
1. Use the formula for the sum of 1 to n and/or the formula for the sum of a geometric sequence to find the following sums: (a) 1+9+92 + ... +9200 (6) 56 + 57 +... + 523 (c) | + 92 + ... + ම ම ම
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with initia [0,1] given by distribution δο and transition matrix 11: Z Z ify=x-1 p 0 otherwise. Use the strong law of large numbers to show that each state is transient. Hint: consider another Markov chain with additional structure but with the same distribution and transition matrix
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with...
use n=6 and p=0.15 to complete parts a through d please
Use n 6 and p 0.15 to complete parts (a) through (d) below. (a) Construct a binomial probability distribution with the given parameters x P(x) 0 0.3771 1 0.3993 2 0.1762 3 0.0415 4 0.0055 5 0.0004 6 0.0000 (Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random variable using #x-O (Round to two decimal places as needed.) x- [x-P(x) and...