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?
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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
Related questions
Question
1. The level of a reactant is random variable X and has the following
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
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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