Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space.Suppose that we also have the following.E(Y)=-6 E(Z) =7Var (X) = 31 Var(Y) = 34 Var(Z)=5E(X)=2Compute the values of the expressions below.E(5-5Y)= 0(")-0%3DVar(3Y+5) = 0E(-x') - 0

GivenE(X)=2E(Y)=-6E(Z)=7Var(X)=31Var(Y)=34Var(Z)=5

Answered: Suppose that X, Y, and Z are jointly…

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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4. (Sec. 5.3) There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose these two variables are independent and identically distributed, each with pmf given in the table below (so X1 and X2 are a random sample of size n = 2). 01 2 P(x) .3 .5 .2 Note that u = 0.9 and o² = .49. (a) Determine the exact pmf of the total number of stops at traffic lights during the commute, To = X1 + X2. (b) Calculate µT, - How does it relate to µ, the population mean? (c) Calculate o. How does it relate to o², the population variance? (d) Let X3 and X, be the number of lights at which a stop is required when driving to and from work on a second day, assumed independent of the first day. With To =the sum of all four X;'s, what now are the values of E[T,] and V[To]?
Can help explain why the other options are correct and why this option is incorrect? Thank you!
Q6. For two random variables X and Y, fxy(x, y) = 0.5 8(x+1) &(y)+0.1 8(x) 8{y) + 0.1 8(x) 8(y-2) + 0.4 &(x-1) S(y+2) + 0.2 &x– 1) d(y – 1) + 0.5 8(x – 1) 8(y – 3). Find, (a) The correlation
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X = 2N−2N2 - 1. The values of X are given in the table below. Outcome ttt hht tth htt hhh tht hth thh Value of X −1 −5 −1 −1 −13 −1 −5 −5 Calculate the probabilities P (X = x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P (X = x)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-9 E (Z) = 1 E (Y)=-6 Var(Y)=28 Var(Z) = 47 Var (X)=44 Compute the values of the expressions below. E (2-Z) = 0 E(X+32)=0 -5 -2-Var(4X) = 0 E(-x²) = 0 Continue □ X S M 31 Ⓒ2022 McGraw Hill LLC. All Rights Reserved
3. Let X₁, X2,..., Xn be iid random variables with mean and variance o2. Define the random variable X-L Z o/√√n where X = (X₁ + X2 + ... + Xn). Find the mean and variance of Z.
If x, x2 ... Xn is a random sample from N (µ, o²) popula- tion, find súfficient estimator for µ and ơ.
Let X be a random variable such that P(X) = 0.25 for x = 1,2, 3, 4. What is P(5)?
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-6 E(Y)=-9 E(Z)=3 Var (X)=8 Var (Y)=14 Var (Z)=25 Compute the values of the expressions below. E (-1- 37) - I -2x - 5z 4 Var (47) - 2 - I e(32°) - [I Dlo
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N² -6N-1. The values of Xare given in the table below. Outcome thh tth hhh hth ttt htt hht tht Value of X -5 -5 − 1 -5 −1 -5 -5 -5 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 8 X
(b) M is discrete random variable that has the expected value 25 and variance 3. Find: i. E(3M +24) ii. Var (2M – 14) + E(4M)

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