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Suppose a pitcher has three distinct pitches to select from. Assuming the pitcher only needed to throw three pitches to get a batter out let X be a random variable representing the number of types of pitch not needed to get a batter out.
P(X=0)= 2/9
P(X=1)= 6/9
P(X=2)= 1/9
Let Y be the number of pitch types the player used to get the batter out.
Please use at least five digits after the decimal point if rounding.
a. What is E[Y], the expected number of pitch types used to get this batter out?
b. What is the standard deviation of ( -6Y^2)?
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