A fair die is rolled 8 times.
a. What is the probability that the die comes up 6 exactly twice?
b. What is the probability that the die comes up an odd number exactly five times?
c. Find the mean number of times a 6 comes up.
d. Find the mean number of times an odd number comes up.
e. Find the standard deviation of the number of times a 6 comes up.
f. Find the standard deviation of the number of times an odd number comes up.
Let X be the number of times the die comes up 6, and let Ybe the number of times the die comes up an odd number. Then X ~ Bin(8,1/6) and Y ~ Bin(8,1/2).
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