Q.2. Consider the random variable described by the probability distribution show

Question

Q.2. Consider the random variable described by the probability distribution shown below: 1 2 3 4 5 2 0.2 0.3 0.2 0.2 0.1 Look at the following Mother Table refer to the table on pp. 5 of Lecture Note #18 if a sample of n 2 observations are drawn from the population of the random variable: Sample Probability LTE Sample Probability 1,1 0.04 34 0.04 1,2 0.06 3,5 0.02 1,3 0,04 41 0.04 1.4 0.04 4.2 0.06 1,5 0.02 43 0.04 2,1 0.06 4,4 0.04 2,2 0.09 l 4,5 0.02 23 0.06 51 0.02 52 2,4 0.06 0.03 2,5 0.03 5.3 0.02 3,1 0.04 54 0.02 32 0.06 5.5 0.01 0.04

Explanation / Answer

a)

b)

The distribution of mean X-bar is

c) P(X-bar >= 4.5) = P(X-bar = 4.5) + P(X-bar =5)

= 0.04 + 0.01 = 0.05

Sample Probability X-bar 1 1 0.04 1 1 2 0.06 1.5 1 3 0.04 2 1 4 0.04 2.5 1 5 0.02 3 2 1 0.06 1.5 2 2 0.09 2 2 3 0.06 2.5 2 4 0.06 3 2 5 0.03 3.5 3 1 0.04 2 3 2 0.06 2.5 3 3 0.04 3 3 4 0.04 3.5 3 5 0.02 4 4 1 0.04 2.5 4 2 0.06 3 4 3 0.04 3.5 4 4 0.04 4 4 5 0.02 4.5 5 1 0.02 3 5 2 0.03 3.5 5 3 0.02 4 5 4 0.02 4.5 5 5 0.01 5

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