Use the result of Exercise 7.45 to show that, if n independent random variables Xi have normal distributions with the means µi and the standard deviations σi, then Y = α1X1 + α2X2 + · · · + anXn has a normal distribution. What are the mean and the variance of this distribution?
Answer to relevant QuestionsIn Exercise 3.101 on page 108, the price of a certain commodity (in dollars) and its total sales (in 10,000 units) were denoted by P and S. Use the joint density given in that exercise and the distribution function technique ...The percentages of copper and iron in a certain kind of ore are, respectively, X1 and X2. If the joint density of these two random variables is given by Use the distribution function technique to find the probability density ...A lawyer has an unlisted number on which she receives on the average 2.1 calls every half– hour and a listed number on which she receives on the average 10.9 calls every half– hour. If it can be assumed that the numbers ...If X is the number of 7’s obtained when rolling a pair of dice three times, find the probability that Y = X2 will exceed 2. Explain why, when we sample with replacement from a finite population, the results of Theorem 8.1 apply rather than those of Theorem 8.6.
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