Suppose a baseball player had 205 hits in a season. In the given probability distribution, the random variable X represents the number of hits the player obtained in a game.
X = 0
PX = .1698
x = 1
PX = .4974
x = 2
PX = .2112
x = 3
PX = .1016
x = 4
PX = .0127
x = 5
PX = .0073
a) compute and interpret the mean of the random variable x (round to one decimal as needed)
b) Which of the following interpretation of the mean is correct?
1. As a number of experiments (n) increases, the mean of the observation will approach the mean of the random variable.
2. The observed value of the random variable will be less than the mean of the random variable in most experiments.
3. As the number of experiments n decreases, the mean of the observations will approach the mean of the random variable.
4. The obsreved value of the random variable will be equal to the mean of the random variable in most experiments.
c) Compute the standard deviation of the random variable x. (round to one decimal)