Suppose a baseball player had 240 hits in a season. In the given probability dis

Question

Suppose a baseball player had 240 hits in a season. In the given probability distribution, the random variable X represents the numbe Compute and interpret the mean of the random variable X. mu_x = 1.4 (Round to one decimal place as needed.) Which of the following interpretation of the mean is correct? The observed value of the random variable will almost always be less than the mean of the random variable. The observed value of the random variable will almost always be equal to the mean of the random variable. As the number of trials n decreases, the mean of the observations will approach the mean of the random variable. As the number of trials n increases, the mean of the observations will approach the mean of the random variable. Compute the standard deviation of the random variable X. sigma_x = (Round to one decimal place as needed.)

Explanation / Answer

Consider:

a)

Thus,  
  
E(x) = mean = Sum(xP(x)) =    1.3944 [ANSWER]

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OPTION D: As the number of trials n increases, the mean of the observations will approach the mean of the random variable. [ANSWER]

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b)

As

Var(x) = E(x^2) - E(x)^2 =    1.06784864

Then

s(x) = sqrt [Var(x)] =    1.033367621 [ANSWER]

x P(x) x P(x) x^2 P(x) 0 0.1677 0 0 1 0.4468 0.4468 0.4468 2 0.2631 0.5262 1.0524 3 0.0842 0.2526 0.7578 4 0.0222 0.0888 0.3552 5 0.016 0.08 0.4

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