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?
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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I need perfect solution for this question parts a, b ,c and d
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
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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