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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? 0.6875 b) What is the probability that X < 2.5? 0.3125 c) What is the probability that 1.25 < X < 2.75? 0.444 d) What is the expected value of X? 0.091 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?

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? 0.6875 b) What is the probability that X < 2.5? 0.3125 c) What is the probability that 1.25 < X < 2.75? 0.444 d) What is the expected value of X? 0.091 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?

A First Course in Probability (10th Edition)
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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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? 0.6875 b) What is the probability that X < 2.5? 0.3125 c) What is the probability that 1.25 < X < 2.75? 0.444 d) What is the expected value of X? 0.091 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? .7 k) What is the probability that X is within 0.1 of its expected value? 1) What is the probability that X = 0.7?
Transcribed Image Text: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? 0.6875 b) What is the probability that X < 2.5? 0.3125 c) What is the probability that 1.25 < X < 2.75? 0.444 d) What is the expected value of X? 0.091 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? .7 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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