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Chapter 5: Q. 5.1 (page 215)
The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by
whereanddenote, respectively,
Boltzmann鈥檚 constant, the absolute temperature of the gas,
and the mass of the molecule. Evaluate in terms of.
Therefore in terms ofthen.
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A randomly chosen test taker obtains a score that is approximately a normal random variable with mean and standard deviation . What is the probability that the score of such a person is
(a) more than 125;
(b) between and ?
Suppose that X is a normal random variable with mean . If , approximately what is ?
The annual rainfall (in inches) in a certain region is normally distributed with . What is the probability that starting with this year, it will take more than years before a year occurs having a rainfall of more than inches? What assumptions are you making?
The density function of is given by
role="math" localid="1646816210505"
Ifrole="math" localid="1646816286362" , find.
Let be a lognormal random variable (see Example 7e for its definition) and let be a constant. Answer true or false to the following, and then give an explanation for your answer.
(a) is lognormal;
(b) is lognormal.
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