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Chapter 5: Q. 5.19 (page 216)
If is an exponential random variable with mean , show that
Hint: Make use of the gamma density function to evaluate the preceding.
The statement has been proved true, i.e.
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Show that.
Hint: Show that
At a certain bank, the amount of time that a customer spends being served by a teller is an exponential random variable with mean minutes. If there is a customer in service when you enter the bank, what is the probability that he or she will still be with the teller after an additional minutes?
A model for the movement of a stock supposes that if the present price of the stock is , then after one period, it will be either with probability or with probability . Assuming that successive movements are independent, approximate the probability that the stock鈥檚 price will be up at least percent after the next periods if
An image is partitioned into two regions, one white and the other black. A reading taken from a randomly chosen point in the white section will be normally distributed with and , whereas one taken from a randomly chosen point in the black region will have a normally distributed reading with parameters . A point is randomly chosen on the image and has a reading of . If the fraction of the image that is black is , for what value of would the probability of making an error be the same, regardless of whether one concluded that the point was in the black region or in the white region?
Twelve percent of the population is left handed. Approximate the probability that there are at least lefthanders in a school of students. State your assumptions.
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