**Problem Statement:**The random variables \( x_i \) are i.i.d. (independently and identically distributed) and uniform in the interval \((-0.5, 0.5)\). Show that:\[E((x_1 + x_2 + x_3)^4) = \frac{13}{80}\]

It is given that the random variables X1, X2, X3 are i.i.d and follow Uniform distribution with…

Answered: The random variables x, are i.i.d. and…

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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Consider the probability distribution for the number of red balls when 4 balls are selected at random from a box consisting of 5 red balls and 4 purple balls. Let the random variable X represents the number of red balls. a) Find F(0) b) Determine P(X≤3) c) Determine P'(X≤4) d)Determine P'(5) e) What is the value of random variable X if F(x) = 9/14?
A kindergarten class consists of 12 boys and 4 girls. The children are arranged from tallest to shortest. Assume that all 16! rankings are equally likely, and no two children are the exactly the same height. let the random variable X be the rank of the second tallest boy. assume that the tallest person in the class is rank 1. (a) find f(x) (b) Calculate E[X] and V[X]
Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
A deck has only 51 cards left, because a spade has been removed. From this deck, cards will be drawn at random, in succession, without replacement. Let Xi be a random variable representing the number of spades in the future i th draw. Calculate the following, and present your answer with 5 digits after the decimal point: Prob(X1 + ... + X7 = 3) = [1]
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.
Let Z be a random variable with E(Z) = 12 and Var(Z) = 5. Based on the statement above, determine which of the following statements are true and false. Show complete solution. a) E(3Z + 10) = 46 b) E(Z^2) = 160 c) Var(10)=10
Suppose X is a random variable such that E(X) = 90 and Var(X) = 7. Compute thefollowing: E(4X + 12) Var(−X) SD(4X)E(X^2) E(X + 3)^2
Two random variables X and Y have joint char- acteristic function l@,,m)=exp(-20,?-80;) (i) Show that X and Y are zero mean ran- dom variables.
Choose points from (0, 1) uniformly and add the numbers together. Stop this process when your add is greater than one. Let N be the random variable which is the number of points that you selected. Find E(N).
Exercise 10. For an exponential random variable X (Definition 10), show that E[X] = }. More generally, for a function o : R R, E(¢(X)] = | (u) dF(u) (5.4)
The time between successive requests to a server are independent random variables, each exponentially distributed with mean 2 (so parameter 1/2). Let Tn denote the time of the nth request. What are the mean and variance of Tn? 2, n On, n² ● 2n, 4n 2n, 4n² None of the other choices.

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The random variables x, are i.i.d. and uniform in the interval (-0.5, 0.5). Show that 13 E{(x₁+x2 + x3)} =