help me find point a-p are independent. distribution or otherwise state "unknown." that X, ~, ΝΟμ,...
Suppose that Xi ~ N(, ?2), i-l, are independent. State the distribution of each of the following variables if it is a "named" distribution or otherwise state "unknown." 15. , n and Z1 ~ NO, l), i 1, , k, and all variables
Only need parts c, e, j, m, and p only need parts c, e, j, m, and p 15. Suppose that X i ~ N(, σ*), i = 1, . . . , n and Zi ~ N(0, 1), i-1, , k, and all variables independent. State the distribution of each of the following variables if it is a "named" distribution or otherwise state "unknown." (a) X1-X2 (i) (b) X2 + 2X3 () Z2 We were unable to transcribe this...
2. Suppose Yi,.. narei normal random variables with normal distribution with unknown mean and variance, μ and or. Let Y-욤 Σ;..x. For this problem, you may not assume that n is large. (a) What is the distribution of Y? (b) what is the distribution of z-(yo), (en, (n-) (c) what is the distribution of (n-p? (d) What is the distribution of Justify your answer. (e) Let Zi-(ga)' + (-)' + (yo)", z2 = (속)' + (n-e)' what is the distribution...
Practice problems using various statistical methods If n independent random variables X have normal distributions with means μ and the standard deviations σ , then determine the distribution of a. I. X-E(X) var(X) C. 2. If n independent random variables Xi have normal distributions with means μί and the standard deviations σί, then determine the distribution of a. b. Y -a1X1 + a2X2+ + anXn (ai constant) X-E(X) Vvar(X) 3. What is CLT? Proof briefly? What are t-, Chi-squared- and...
Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random variables with mhean μ and variance a) Compute the expected value of W b) For what value of a is the variance of W a minimum? σ: Let W-aX + (1-a) Y, where 0 < a < 1. Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random...
3. Suppose Xi, X2, and X are independent random variables drawn from a binomial distribution with parameters p and n. The observed values are Xi -3, X2-4, and (a) Suppose n 12 and p is unknown. What is the maximum likelihood estimator (b) Suppose p - 0.4 and n is unknown. What is the maximum likelihood estimator for p? for n? (Note: Since n is discrete you can't use calculus for this; just write the formula and use trial and...
iid Let X1,, X, ^ X~P for some unknown distribution P with continuous cdf F. Below we describe a ? test for the null and alternative hypotheses We divide the sample space into 5 disjoint subsets refered to as bins A1(-00,-2), A2 -(-2,-0.5), As -(-0.5,0.5), A4 (0.5,2) As -(2, oo). as functions of X, by Now, define discrete random variables For example, if Xi --0.1, then Xi є Аз and so Y;-3. In other words, Y, is the label of...
(15 points) Consider two independent, exponential random variables X,Y ~ exp(1). Let U = X + Y and V = X/(X+Y). (a) (5 points) Calculate the joint pdf of U and V. (b) (5 points) Identify the distribution of U. If it has a "named” distribution, you must state it. Otherwise support and pdf is enough. (c) (5 points) Identify the distribution of V.If it has a "named” distribution, you must state it. Otherwise support and pdf is enough.
4. Suppose X1, . . . ,X, are independent, normally distributed with mean E(Xi) and variance Var(X)-σί. Let Żi-(X,-μ.)/oi so that Zi , . . . , Ζ,, are independent and each has a N(0, 1) distribution. Show that LZhas a x2 distribution. Hint: Use the fact that each Z has a xî distribution i naS
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...