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(Y)=-5 E(Z)=-1Var(X)=3Var(Y)=1Var(Z)= 34Compute the values of the expressions below.E (-5-3X)= D-4Z-4XE-4Var(-4+Z)= ]E(-31²) = 0

Given that, E(X) =-9 , E(Y) =-5, E(Z) =-1 Var(X) =3, Var(Y) =1, Var(Z) =34

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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- 6 Suppose X ~ N(2, 9) and Y ~ N(2, 16) are independent random variables. Then P(X + Y > -10) equals: ut of Select one: а. 0.1587 question b. 0.1151 С. О.5 d. 0.8413 e. 0.8849
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2. Let X be a binomial random variable with E(X) = 30 and Var(X) = 21. Find the parameters n and p of X.
I'm trying to find the variance of a sample, and I seem to find two different formulas--one involving dividing by n-1, and another by n(n-1). Attached is the one with the n(n-1) in the formula (disregard the number 30 in the image). Which one is correct? My guess is they're both correct. It's just I don't see what the difference between the two forms is.
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3) A random variable X takes the values 0, 2 and 3 with probabilities 0.3, 0.1 and 0.6, respectively. A random variable in the form of Y = 3(X-1)2 is defined. a) Find the expected value and variance of the random variable X. b) Find the variance of the Y random variable. c) Find the cumulative distribution function of the Y random variable.
A scheme of random number generator is described as follows. First, one generates a normal random number with mean 0 and variance 16, a uniform random number on [0,24], then a geometric random number of parameter p = 0.25 (each independently). Then we define the random number to be the average of these three numbers. 30 random numbers are generated with the scheme above, denoted as {X}31. Estimate/approximate the probability that the average 1 X is deviated from μ = E[X₁] by a distance of more than 0.2 using: (a) Chebyshev's inequality; (b) central limit theorem. k=1
Q1:Show that: If X1, X2, , Xn are independent random variables and X = X1 + X2 ++Xn, then Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a die? Q3: Find the expectation and the variance of X, where X is binomial random variable X - Binomial (n, p), Var(X)? 1 Chapter 3 Let X be a discrete random variable with range Rx = {1, 2, 3, ...}. Q4: Suppose the PMF of X is given by 1 for k = 1, 2, 3, ... 2k Px (k) = a) Find and plot the CDF of X, Fx (a). b) Find P(1 < X < 3). Chapter 3 Functions of Random Variables Q5: Example. Let Rx = {0, T T 37 , such that 4'2 4. Find E[sin(X)]. Q6: A machine produces a defected items with a probability of 0.1. What is the probability that in a sample of three item will have at most one item defected? Q7: For any independent X, and Y random variables, E[XY]=E[X]E[Y]. Show that? Q8: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2. 3 Chapter 3
20
1 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.
3b)
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.

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