In the following probability distribution, the random variable X represents the

Question

In the following probability distribution, the random variable X represents the number of activities at least one parent of a K-5^th grade student is involved in. Compute and interpret the mean of the random variable X. mu_x = activities (Round to one decimal place as needed) Which of the following interpretation of the mean is correct? As the number of experiments n decreases, the mean of the observations wiDll approach the mean of the tandem variable The observed value of the random variable will be equal to the mean of the random variable m most experiments The observed value of the random variable will be less than the mean of the random variable in most experiments. As the number of experiments n increases, the mean of the observations will approach the mean of the random variable Compute the variance of the random variable X. sigma^2 = activities^2 (Round to one decimal place as needed) Compute the standard deviation of the random variable X. sigma = activities (Round to one decimal place at needed.)

Explanation / Answer

b)

Consider:

Thus,  
  
u = mean = Sum(xP(x)) =    2.442 [ANSWER]

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Hence, as the number of expriments increases, the mean approaches 2.442, so

OPTION D. [ANSWER]

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c)

Thus,

Var(x) = E(x^2) - E(x)^2 =    2.316636 [ANSWER, VARIANCE]

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d)

Hence,

s(x) = sqrt [Var(x)] =    1.522049933 [ANSWER]

x P(x) x P(x) x^2 P(x) 0 0.196 0 0 1 0.095 0.095 0.095 2 0.132 0.264 0.528 3 0.225 0.675 2.025 4 0.352 1.408 5.632

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