g(x) =34+1if n < x < n + 1given this functionfor all nonnegative integers n=0,1,2,3,... and g(x)=0 otherwise. (Hint: I strongly suggest that yougraph this function.)1. Can px(n)=g(n) be the probability mass function of a discrete random variable X that takesvalues in Z? If not, why, and if so, solve the E[X] and Var(X).2. Can pY(y)=g(y) be the probability density function of a continuous random variable Y? If not,explain why, and if so, compute E[Y] and Var(Y).

Given that the function is, gx=34n+1, n≤x<n+1, n=0,1,2,3,.... 1. pX(n)=g(n) Let us check g(n) is…

Answered: 1. Can pX(n)=g(n) be the probability…

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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2. a. If X is a discrete random variable with probability mass function P(X =x) and a, b are constants, prove that E(aX +b)= aE(X)+b, ii. Var (ax +b)=a³Var(X). i.
4. Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X))> log(1/E(X)) (d) E(X³) > (E(X))³
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The probability that none of the three bulbs in a set of traffic lights will have to be replaced during the first 1200 hours of operation if the lifetime X of a bulb (in thousands of hours) is a random variable with probability density function f(x) = 6[0.25-(x-1.5)2] when 1 ≤ x ≤ 2 and f(x) = 0 otherwise is
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Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x

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1. Can pX(n)=g(n) be the probability mass function of a discrete random variable X that takes values in Z? If not, why, and if so, solve the E[X] and Var(X).