Concept explainers
The pH of water samples from a specific lake is a random variable Y with
a Find E(Y) and V(Y).
b Find an interval shorter than (5, 7) in which at least three-fourths of the pH measurements must lie.
c Would you expect to see a pH measurement below 5.5 very often? Why?
a.
Compute the value of
Compute the value of
Answer to Problem 33E
The value of
The value of
Explanation of Solution
The probability density function is given below:
The value of
Thus, the value of
The value of
The variance of Y is,
Thus, the variance of Y is 0.15.
b.
Compute the interval shorter than (5,7), within which, at least three-fourths of the pH measurements must lie.
Answer to Problem 33E
The interval shorter than (5, 7) at least three-fourths of the pH measurements must lie.
is
Explanation of Solution
From the given information, let X be the random variable be the spread on either side of
Suppose
Then,
Thus, the interval shorter than (5, 7) at least three-fourths of the pH measurements must lie.
is
c.
Explain whether one can expect to see a pH measurement below 5.5.
Answer to Problem 33E
One may expect to see a pH measurement below 5.5 with probability 0.5781.
Explanation of Solution
From the given information, let X be the random variable that is the spread on either side of
The expect to see a pH measurement below 5.5 very often is obtained below:
Thus, one may expect to see a pH measurement below 5.5 with probability 0.5781.
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Chapter 4 Solutions
Mathematical Statistics with Applications
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