Question

Suppose a baseball player had 208 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 1 2 3 4 5 ​P(x) 0.1166 0.4774 0.2601 0.1094 0.0168 0.0197 ​(a) Compute and interpret the mean of the random variable X. mu Subscript xequals nothing ​(Round to one decimal place as​ needed.) Which of the following interpretation of the mean is​ correct? A. The observed value of the random variable will almost always be less than the mean of the random variable. B. The observed value of the random variable will almost always be equal to the mean of the random variable. C. As the number of trials n​ decreases, the mean of the observations will approach the mean of the random variable. D. As the number of trials n​ increases, the mean of the observations will approach the mean of the random variable. ​(b) Compute the standard deviation of the random variable X. sigma Subscript xequals nothing ​(Round to one decimal place as​ needed.)

Answer 1

For calculating mean

use the following formula:

E(X)=∑x⋅p(x)

E(X) = 1.5

The interpretation of mean of random variable is given as D)As the number of trials n​ increases, the mean of the observations will approach the mean of the random variable

Explanation :

The law of large numbers states that the observed random mean from an increasingly large number of observations of a random variable will always approach the distribution mean . That is, as the number of observations increases, the mean of these observations will become closer and closer to the true mean of the random variable.

b) Standard Deviation of the random variable is calculated as follows,

use the following formula:

E(x) = 1.5

SD(X) = 1.0194 1.0