# Linear_Combinations_Day_1.doc - Combinations Day 1 Name...

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Combinations Day 1 Name: ______________________________ Let’s investigate a dice problem. First, find (or recall) the expected value and standard deviation for the roll of one die.E(X) = ______ X= ____________Now…Option 1 is to roll one die and double its value, obtaining 2, 4, 6, 8,10, or 12. Option 2 is to roll two dice and find their sum, obtaining 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12. Option 3 is to roll two dice and find their difference obtaining -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, or 5.a. Write the probability distribution of option 1. Find the mean and standard deviation of the distribution.E(2X) = ______ 2X= ____________b. Write the probability distribution of option 2. Find the mean and standard deviation of the distribution. E(X+X) = ______ XX= ____________c. Write the probability distribution of option 3. Find the mean and standard deviation of the distribution. E(X - X) = ______ XX= ____________d. Compare the means and standard deviation for all three options. e. Come up with a formula for the mean and standard deviation for Option 1, Option 2, and Option 3 in terms of the mean and standard deviation for the roll of one die. E(2X) = _________________ 2X= _________________E(X+X) = _________________ XX= _________________E(X - X) = _________________ XX= _________________If you have just one random variable and you add/subtract a number to the list of data or multiply the entire list by a constant, then youhave performed a linear transformation.