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Chapter 5: Q. 5.18 (page 213)
Suppose that X is a normal random variable with
mean 5. If P{X > 9} = .2, approximately what is Var(X)?
The required variance is.
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A roulette wheel has 38 slots, numbered 0, 00, and 1 through 36. If you bet 1 on a specified number, then you either win 35 if the roulette ball lands on that number or lose 1 if it does not. If you continually make such bets, approximate the probability that
(a) you are winning after 34 bets;
(b) you are winning after 1000 bets;
(c) you are winning after 100,000 bets
Assume that each roll of the roulette ball is equally likely to land on any of the 38 numbers
If is an exponential random variable with a parameter, compute the probability density function of the random variable defined by
The time (in hours) required to repair a machine is an exponentially distributed random variable with parameters. What is
the probability that a repair time exceedshours?
the conditional probability that a repair takes at leasthours, given that its duration exceedshours?
The life of a certain type of automobile tire is normally distributed with mean miles and standard deviation miles.
(a) What is the probability that such a tire lasts more than miles?
(b) What is the probability that it lasts between andmiles?
(c) Given that it has survived miles, what is the conditional probability that the tire survives another miles?
In independent tosses of a coin, the coin landed on heads times. Is it reasonable to assume that the coin is not fair? Explain.
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