3) A high school teacher assigns the students to prepare research homework with proper cita- tions. Homework requires each student to correctly reference at least two sources. Past works show that the number of sources cited is a random variable, X, with probability distribution given in the table below. x | 2 3 4 P(x) | 0.5 0.3 0.2 Suppose a random sample of three student papers is selected. (a) Find the sampling distribution of X, the sample mean number of sources cited (Construct a table for the sample, F and the probability). (b) Find the mean and the variance of the random variable X. (c) Find the mean and the variance of the random variable X .

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3) A high school teacher assigns the students to prepare research homework with
tions. Homework requires each student to correctly reference at least two sources. Past works
show that the number of sources cited is a random variable, X, with probability distribution given
in the table below.
proper
cita-
3
4
p(x) | 0.5
0.3
0.2
Suppose a random sample of three student papers is selected.
(a) Find the sampling distribution of X, the sample mean number of sources cited (Construct a
table for the sample, x and the probability).
(b) Find the mean and the variance of the random variable X.
(c) Find the mean and the variance of the random variable X .
(d) Show the relation between the sample and the population mean, and the sample variance
and the population variance.
Transcribed Image Text:3) A high school teacher assigns the students to prepare research homework with tions. Homework requires each student to correctly reference at least two sources. Past works show that the number of sources cited is a random variable, X, with probability distribution given in the table below. proper cita- 3 4 p(x) | 0.5 0.3 0.2 Suppose a random sample of three student papers is selected. (a) Find the sampling distribution of X, the sample mean number of sources cited (Construct a table for the sample, x and the probability). (b) Find the mean and the variance of the random variable X. (c) Find the mean and the variance of the random variable X . (d) Show the relation between the sample and the population mean, and the sample variance and the population variance.
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