I need perfect solution for this question parts a, b ,c and d 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?

The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=1/(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?

The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=1/(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?

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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