Math 1350 6.1 Bookwork p. 290, #5 Name 6.5 Consider the population described by the probability distribution shown here: x 12345 P(x) 2.3.2.2.1 The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as follows: Sample Probability Sample Probability 1,1 .04 3,4 .04 1,2 .06 3,5 .02 1,3 .04 4,1 .04 1,4 .04 .06 1,5 .02 4,3 .04 2,1 .06 4,4 04 2,2 .09 4,5 .02 2,3 06 5, 1 02 2,4 .06 5,2 .03 2,5 .03 5,3 02 3, 1 .04 5,4 .02 3,2 06 5,5 .01 3, 3 .04 a. Find the sampling distribution of the sample mean z. b. Construct a probability histogram for the sampling distribution of . c. What is the probability that is 4.5 or larger? d. Would you expect to observe a value of equal to 4.5 or larger? Explain. 44444 4,2 UN 55555 RS

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Math 1350 6.1 Bookwork p. 290, #5
Name
6.5 Consider the population described by the probability distribution shown here:
x 12345
P(x) 2.3.2.2.1
The random variable x is observed twice. If these observations are independent, verify that the different samples of
size 2 and their probabilities are as follows:
Sample Probability Sample Probability
1,1 .04
3,4 .04
1,2
.06
3,5
.02
1,3 .04
4,1
.04
1,4
.04
.06
1,5
.02
4,3
.04
2,1 .06
4,4
04
2,2 .09
4,5
.02
2,3 06
5, 1
02
2,4 .06
5,2
.03
2,5 .03
5,3
.02
3, 1 .04
5,4
.02
3,2
06
5,5 .01
3,3 .04
a. Find the sampling distribution of the sample mean z.
b. Construct a probability histogram for the sampling distribution of z.
c. What is the probability that is 4.5 or larger?
d. Would you expect to observe a value of equal to 4.5 or larger? Explain.
44444
4,2
UN
55555
Transcribed Image Text:Math 1350 6.1 Bookwork p. 290, #5 Name 6.5 Consider the population described by the probability distribution shown here: x 12345 P(x) 2.3.2.2.1 The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as follows: Sample Probability Sample Probability 1,1 .04 3,4 .04 1,2 .06 3,5 .02 1,3 .04 4,1 .04 1,4 .04 .06 1,5 .02 4,3 .04 2,1 .06 4,4 04 2,2 .09 4,5 .02 2,3 06 5, 1 02 2,4 .06 5,2 .03 2,5 .03 5,3 .02 3, 1 .04 5,4 .02 3,2 06 5,5 .01 3,3 .04 a. Find the sampling distribution of the sample mean z. b. Construct a probability histogram for the sampling distribution of z. c. What is the probability that is 4.5 or larger? d. Would you expect to observe a value of equal to 4.5 or larger? Explain. 44444 4,2 UN 55555
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