Question

Suppose a baseball player had

229229

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)	0.13590.1359	0.49370.4937	0.26020.2602	0.07830.0783	0.02070.0207	0.01120.0112

​(a) Compute and interpret the mean of the random variable X.

mu Subscript xμxequals=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​ increases, the mean of the observations will approach the mean of the random variable.

D.

As the number of trials n​ decreases, 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 xσxequals=nothing

​(Round to one decimal place as​ needed.)

Answer 1

X	P(X)	x*P(x)	P(x)*(x-μ)^2
0	0.1359	0	0.261742
1	0.4937	0.4937	0.074247
2	0.2602	0.5204	0.09752
3	0.0783	0.2349	0.203516
4	0.0207	0.0828	0.141248
5	0.0112	0.056	0.146137
Total	1	1.3878	0.924411

Mean μ_x = = 1.3878

μ_x = 1.4

As the number of trails n increases, the mean of the observations will approach the mean of the random variable.

b)

Variance = ² = 0.9244

Standard deviation (σ_x) = sqrt ( 0.9244) = 0.9615.

σ_x = 1.