i need perfect solution of e , f , g , h part The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function:f(x)=(x − 1)²(4 - x) for 1 ≤ x ≤ 4 and 0 otherwise.a) What is the probability that X > 2.5? |b) What is the probability that X < 2.5?c) What is the probability that 1.25 < X < 2.75?d) What is the expected value of X?e) What is the expected value of X - 3?f) What is the expected value of 3X?g) What is the expected value of x²?h) What is the probability that X is less than its expected value?i) What is the expected value of √X?j) What is the 70th percentile of X? [k) What is the probability that X is within 0.1 of its expected value?1) What is the probability that X = 0.7?

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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e) What is the expected value of X-3? | f) What is the expected value of 3X? [ g) What is the expected value of x² ?[ h) What is the probability that X is less than its expected value?