Problems 5 and 6 refer to the discrete random variables X and Y whose joint distribution is given in thefollowing table, so P(X = 1 and Y =-1) = 1/4, P(X = 1 and Y = 1) = 0, etc.Y= -1Y = 0Y = 1X = 1X = 2X = 31/41/81/161/161/81/161/161/4lam 5: Comnute thedistrProblem 6: Compute Cov(X, Y) and the correlation p for the random variables X and Y. Are X and Yindependent?

Answered: Image /qna-images/answer/4572f1e1-e41a-48f8-b600-c157136fd3c0.jpg

Answered: Problems 5 and 6 refer to the discrete…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. For each random variable described below, give its distribution (which will be Binomial, Geometric, Hypergeometric, Pascal, or Poisson) and the parameters of that distribution. (a) You are working on a difficult homework assignment with 5 problems. Every minute, you have an idea for the problem you are working on, but it only has a 5% chance of working. If it doesn’t work, you keep working on that problem, and if it works, you move on to the next problem. The random variable W is the time (in minutes) that it takes you to finish the homework assignment. (b) A standard 52-card deck is split equally between two players. The random variable X is the number of aces received by the first player. (There are four aces in the deck.) Note: this is a key parameter when playing the “card game” “War”. (c) Every time you turn on the light, the light bulb has a 1% chance of burning out and you have to replace it. The random variable Y is the number of times you turn on the light before you have…
5. Professor Snape is your instructor for Chemistry 101. He has given the same final exam for his class for a long time; he happens to know that exam scores on this test are normally distributed and have a population mean of µ=80. Because of prior laboratory catastrophes (don’t worry, all students were returned to their original species), he tried a new method of instruction this year. He got a random sample of n=16 students and taught them using virtual reality (VR). These students then took his original final exam, and their sample average was M=76. Assume for this first question that Snape’s final exam has a population standard deviation of σ=12. Can he demonstrate that the VR instruction method was significantly different from his traditional teaching method? (Assume a two-tailed test with α=.05) No, he cannot conclude that his VR method is significantly different from his traditional method. This is because the z-test equals -1.00 and is not significant…
The answer is 23
Problem 1: Let X and Y be independent random variables following Poisson distributions, each with parameter 1 = 1. Show that the distribution of Z = X+ Y is Poisson with parameter à = 2. Hint: •G) =
Problem 12 Let X and Y be two independent random variables with PMFS for x = 1, 2, 3, 4, 5 Px(k) = Py(k) = %3| otherwise Define Z = X – Y. Find the PMF of Z.
2 This is a more general version of Problem C.1. Let Y1, Y2, ..., Y, be n pairwise uncorrelated random variables with common mean m and common variance o. Let Y denote the sample average. (i) Define the class of linear estimators of u by W. = a,Y, + a,Y, + ..+ a,Y. where the a, are constants. What restriction on the a, is needed for W to be an unbiased estimator of u? (ii) Find Var( W.). Math Refresher C Fundamentals of Mathematical Statistics 745 For any numbers a1, az, ..., a, the following inequality holds: (a, + a, + ... + a,}/n s a + a + + a. Use this, along with parts (i) and (ii), to show that Var( Wa) = Var(Y) whenever W is unbiased, so that Y is the best linear unbiased estimator. [Hint: What does the inequality become when the a, satisfy the restriction from part (i)?] (iii)
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Question 5 Suppose that the random variables X₁,..., X and Y₁,...,Y, are random sample from independent normal distributions N(3,8) and N(3,15), respectively.
Problem 7 Let X ~ Poisson(a) and Y ~ Poisson(3) be two independent random variables. Define a new random variable as Z = X +Y. Find the PMF of Z.

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