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?
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?
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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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a41257f-c9b6-4487-97a2-e459f9e4d541%2F0e3aaea2-c12e-44ea-8287-88064c090e7d%2Fczofom_processed.png&w=3840&q=75)
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? |
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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