Suppose a baseball player had 224 hits in a season. In the given probability dis

Question

Suppose a baseball player had 224 hits in a season. In the given probability distribution, the random variable X represents the number of hits the player obtained in a game. (a) Compute and interpret the mean of the random variable X. mu_x = hits (Round to one decimal place as needed.) Which of the following interpretation of the mean is correct? A. As the number of experiments increases, the mean of the observations will approach the mean of the random variable. B. The observed value of an experiment will be equal to the mean of the random variable in most experiments. C. The observed value of an experiment will be less than the mean of the random variable in most experiments. D. As the number of experiments 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_x = hits (Round to one decimal place as needed.)

Explanation / Answer

a)

mean of random variable X = 0*0.1292+1*0.4292+2*02134+3*01407+4*0.0521+5*0.354 = 3.2565 ~ 3.3

b)

asnswer is (A) i.e as the number of experiments increase , the mean of the observations will approach the mean of the mean of the random variabe

c)variance of random variable X = (0-3.3)2*0.1292+(1-3.3)2*0.4292+(2-3.3)2*0.2134+(3-3.3)2*0.1407+(4-3.3)2*0.0521+(5-3.3)2*0.354 = 5.0994

standard deviaton of random variable X = variance = 5.0994 = 2.2582 ~ 2.3

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