Calculate the variance of the random variable g(X) in The hospital period, in days, for patients following treatment for a certain type ofkidney disorder is a random variable Y = X + 4, where X has the density function32x > 0(x + 4)3'0, elsewheref(x) =Find the average number of days that a person is hospitalizedtreatment for this disorder.following

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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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Let X be a discrete random variable that is the value shown on a single roll of a fair die. (a) What is the expected value of X? Explain the meaning of E(X) in this case. (b) Find the expected value of X². (c) Find the variance of X. (a) (b) (c)
Practice Question 2: Let X₁ a random variable with expected value (mean) E(X₁) = 17 and variance V(X₁) = 12. Let X₂ another random variable with expected value (mean) E(X₂) = 22 and variance V(X₂) = 16. The covariance between X₁ and X₂ is Cov(X1,X 2)=9. Let a new random variable Y defined as Y = 9X₁ + 10x₂. a. d. Explain briefly the meaning of the correlation of these two random variables X₁ and X2. e. Explain briefly if X₁ and X₂ are linearly independent not.
show that if X11, X12,..., X1, X21, X22,..., X2n₂ are independent random variables, with the first n constitut- ing a random sample from an infinite population with the mean μ₁ and the variance of and the other n2 constitut- ing a random sample from an infinite population with the mean μ2 and the variance o2, then 1 M2 (a) E(X₁-X₂) = μ₁ −μ2; 07 0 22 (b) var(X₁-X₂) = + n₁ n₂
Without using a moment generating function; Prove that the variance of a beta-distributed random variable with parameters α and β is σ2 = αβ/[(α + β)^2 (α + β + 1)]
Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter 0 > 0 is defined by F(x; θ) - 1-el x > 0 i) What is the expected value of X,E(X)? ii) What is the variance of X,V(X)?
Consider a random variable V modeling the version of the software that people have installed on their computers, where the possible versions are {1, 2, 3, 4}. People are equally likely to have versions 1 and 2 and also equally likely to have versions 3 and 4. People are also x times more likely to have version 3 than version 2. (a) What is the (probability mass function) PMF of V as a function of x (b) What is the expected version of the software. Hint: the expected value of V as a function of x (c) What is the minimum value of x to ensure that the mean version is at least version 3?
Two random variables X and Y have means X = 1 and Y=2, variances o=4 and o X and Pxy = 0.4. New random variables W and V are defined by V =−X+2Y and W = X +3Y. Find (a) the means, (b) the variances, = 1,
Three statistically independent random variables X₁, X₂ and X₂ have mean values X₁ =3, X₂ = 6 and X₂ = -2. Find the mean values of the following functions: 1 2 (a) (b) g(X₁, X₂, X3)= X₁ +3X₂ + 4X3 29 g(X₁, X₂, X3) = X₁X₂X₂ 29
Let a mixed random variable X have the following distribution. Find expectation of X. Find variance of X.
ans Theorem 9.3. Let X and Y be independent random variables with finite variances, and a, b ER. Then Var(aX) = a²Var (X), Var (X+Y) = VarX + Var Y, Var (ax + bY) = a²VarX + b²Var Y. sercise Prove the theorem. Remark 9.2. Independence is sufficient for the variance of the sum to be equal to the sum of the variances, but not necessary. Remark 9.3. Linearity should not hold, since variance is a quadratic quantity. Remark 9.4. Note, in particular, that Var (-X) = Var(X). This is as expected, since switching the sign should not alter the spread of the distribution.
Suppose that the number of customers entering a bank in one hour is a Poisson random variable and suppose that P(X=0)=0.02. Find the mean and variance of the variable. X: Number of customers entering a bank in one hour E(X)= Answer (Give the exact answer) V(X)= Answer (Give the exact answer) What is the probability that 5 customers will enter in two hours? Answer: Note: Answer with at least 4 decimal places
x p(x) -1 1/7 0 3/7 2 2/7 4 1/7 What is the expected value or mean of x? What is the variance of x?

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