Answered: 1. The level of a reactant is random…

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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Related questions

Question

1. The level of a reactant is random variable X and has the following probability density function:
f(x)=

2e^−2x

1−e⁻²

for

0 ≤ x ≤ 1

and 0 otherwise.

a) What is the probability that X > 0.6?

b) What is the probability that X < 0.4?

c) What is the probability that 0.3 < X < 0.5?

d) What is the expected value of X (E(X))?

e) What is the expected value of X - 2?

f) What is the expected value of 3X?

g) What is the expected value of

X²

?

h) What is the probability that X is greater than its expected value?

i) What is the expected value of

X³+2X−3

?

j) What is the 73rd percentile of X?

k) What is the probability that X is within 0.11 of its expected value?

l) What is the variance of X?

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