Suppose a pitcher has three distinct pitches to select from. Assuming the pitcher only needed to throw three pitches to get a batter out letXbe a random variable representing the number of types of pitchnotneeded to get a batter out.

P(X=0)=2/9

P(X=1)=6/9

P(X=2)= 1/9

Let Ybe the number of pitch types the player used to get the batter out.

Please useat leastfive 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)?