1. The error, X, in measuring the length of a rivet (in micrometers) has the following probability density functionf(x)= 20·x·(3−x)^3/243 for 0 ≤ x ≤ 3 and 0 otherwise.e) What is the expected value of X - 3? f) What is the expected value of 6X? g) What is the expected value of X2? h) What is the probability that X is greater than its expected value? i) What is the expected value of X3−3X+1? j) What is the 55th percentile of X? k) What is the probability that X is within 0.4 of its expected value? l) What is the probability that X = 2?

by bartleby policy i can gives only 3 subparts at a time here first we have to find expected value…

Answered: e) What is the expected value of X - 3?…

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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1. The error, X, in measuring the length of a rivet (in micrometers) has the following probability density function
f(x)= 20·x·(3−x)^3/243 for 0 ≤ x ≤ 3 and 0 otherwise.

e) What is the expected value of X - 3?

f) What is the expected value of 6X?

g) What is the expected value of X²?

h) What is the probability that X is greater than its expected value?

i) What is the expected value of X³−3X+1?

j) What is the 55th percentile of X?

k) What is the probability that X is within 0.4 of its expected value?

l) What is the probability that X = 2?

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