SOLVE STEP BY STEP IN DIGITAL FORMATÿ »Ü ¸♥286. Let X be a random variable with distribution Ber(p) and let a and b betwo constants with a 0. Define the random variable Y = ax + b. finda) The probability function of Y.b) E(Y).c) Var(Y).d) E(Y) for n = 1, 2,...

Given information: X~Ber(p) a and b are constant with a=0 Define, Y=aX+b Find: a)The probability…

Answered: 286. Let X be a random variable with…

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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10. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf f₂ (ylx) of Y.. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours. d) Given that a Type B bulb fails at 300 hours, find the probability that a Type A bulb lasts longer than 300 hours. e) What is the expected total lifetime of two Type A bulbs and one Type B bulb?
4.) Classify each of the following random variables as discrete or continuous. a.) X = the number of eggs that a hen lays in a day b.) Y = the amount of milk a cow produces in a day c.) W = the measure of voltage for a smoke-detector battery d.) M = the count of the number of patrons attending a rock concert e.) C = the cost of a randomly selected textbook f.) X = the time it take to fill %3D %3D %3D %3D %3D can of soda
Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are constant random variables.
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Suppose that three random variables x,„X,„X, fom a random sample from the uniform distribution on the interval [0,2], and they are independent. Determine the value of E(2X, –3X, +X,-4). Var(2X,–3X,+X, -4) and E(2x, –3X, +X, -4)°]
Let the probability function of the random variable X bef(x) = { x/45 if x = 1, 2, 3, ⋯ ⋯ ,9 { 0 otherwiseFind E(X) and Var(X)
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Exercise 3. Let X be a random variable with mean and variance o². For a € R, consider the expectation E((X-a)²). a) Write E((X-a)²) in terms of a, u and o². b) For which value a is E((X - a)²) minimal? c) For the value a from part (b), what is E((X-a)²)?
Let X ~ N(1,2) and Y ~ N(4, 7) be independent random variables. Find the probability P(X + Y > 0):
For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. (d) X = the length of a randomly selected rattlesnake Describe the set of possible values for the variable. 0, 1, 2, 3, ... 1, 2, 3, ... [0, ∞) (0, ∞) State whether the variable is discrete. discrete not discrete (e) Z = the sales tax percentage for a randomly selected amazon.com purchase, where n = the total number of possible sales tax percentages for online purchases Describe the set of possible values for the variable. z1, z2, z3, ..., zn [0, zn] 1, 2, 3, ..., n [0, n] State whether the variable is discrete. discrete not discrete (f) Y = the pH of a randomly chosen soil sample Describe the set of possible values for the variable. 0, 1, 2, 3, ..., 14 [0, 14] 1, 2, 3, ..., 14 (0, 14] State whether the variable is discrete. discrete not discrete (g) X = the tension (psi) at which a randomly selected…

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286. Let X be a random variable with distribution Ber(p) and let a and b be two constants with a 0. Define the random variable Y = ax + b. find a) The probability function of Y. b) E(Y). c) Var(Y). d) E(Y) for n = 1, 2,...