27 Suppose X is a random variable with a mean of 10 and a variance of 100

# 27 suppose x is a random variable with a mean of 10

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27. Suppose Xis a random variable with a mean of 10 and a variance of 100. Suppose Yis arandom variable with a mean of 2 and a standard deviation of 16. Also, suppose Xand Yare independent. What is the variance of –2X?Must show calculations.28.Explain the law of large numbers.29.In order for the law of large numbers to apply, ___________.A)observations must be independentB)observations must be dependentC)observations can be dependent as long as the dependence dies out fast enough as you take measurements farther apart in timeD)None of the abovePage 9
30.Fill in the blank. The mean of a random variable is also called the _______.31.When applying the law of large numbers, how many trials are needed to ensure that the mean of an outcome is close to the population mean?32.The correlation between two independent random variables is ______.33.The variance of any fixed number ais ______.34.The mean of any fixed number ais ______.A)aB)0C)1D)a235.Adding a constant ato any random variable will change the mean by a value of _____.Page 10
36.Adding a constant ato any random variable will change the standard deviationby a value of _____.37.Correlation is a measure of ________.38.When two random variables are not independent, the variance between the two random variables depends on the _____.A)correlationB)independenceC)variabilityD)None of the abovePage 11

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