An investor buys a stock and keeps it for 12 months. At the end of each month, he records whether it went up or down that month. Define a random variable X; = 1 if the stock went up in the i-th month and X; = Oif it did not go up. Suppose the probability that this stock goes up in a month is 0.75. Show your work for the following questions. 1. What is the mean (expected value) of X1? 2. What is the standard deviation of X1? 3. Find the mean of Y = X1 + X2 + .. + X12. Use the rules for means. %3D 4. Suppose that all of the X;s are independent of each other. Find the standard deviation of Y = X1 + %3D X2 +...+X12. Use the rules for variances.
An investor buys a stock and keeps it for 12 months. At the end of each month, he records whether it went up or down that month. Define a random variable X; = 1 if the stock went up in the i-th month and X; = Oif it did not go up. Suppose the probability that this stock goes up in a month is 0.75. Show your work for the following questions. 1. What is the mean (expected value) of X1? 2. What is the standard deviation of X1? 3. Find the mean of Y = X1 + X2 + .. + X12. Use the rules for means. %3D 4. Suppose that all of the X;s are independent of each other. Find the standard deviation of Y = X1 + %3D X2 +...+X12. Use the rules for variances.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:An investor buys a stock and keeps it for 12 months. At the end of each month, he records whether it went up
or down that month. Define a random variable X; = 1 if the stock went up in the i-th month and X; = 0 if
%3D
it did not go up. Suppose the probability that this stock goes up in a month is 0.75. Show your work for the
following questions.
1. What is the mean (expected value) of X1?
2. What is the standard deviation of X1?
3. Find the mean of Y =X1+X2+ .+X12. Use the rules for means.
||
...
4. Suppose that all of the X;'s are independent of each other. Find the standard deviation of Y = X1 +
X2 +..+X12, Use the rules for variances.
%3D
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