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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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a41257f-c9b6-4487-97a2-e459f9e4d541%2Fb6762168-b05e-4313-8ef5-895f745709ca%2Fn6s9kel_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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i need same explanatory answer of part j , k and l
![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?](https://content.bartleby.com/qna-images/question/4a41257f-c9b6-4487-97a2-e459f9e4d541/0f9a28c4-e242-43c2-b4e3-a0e537d63026/lxurwxd_thumbnail.png)
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?
Solution
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