For the population of Cal Poly students, let X = number of hours slept in the...

For the population of Cal Poly students, let X = number of hours slept in the last 24 hours and Y = number of exams today. Consider the following (admittedly simplistic) joint probability distribution for Xand Y.

			x
		5	6	7	8
	0	.01	.09	.16	.18
y	1	.11	.06	.04	.02
	2	.28	.02	.02	.01

For your convenience, I have calculated the following: ?(?)=6.24,?(?2)=40.34,?(?)=0.89,?(?2)=1.55E(X)=6.24,E(X2)=40.34,E(Y)=0.89,E(Y2)=1.55.

A. Determine the marginal distribution of X.

B. Calculate E(XY).

C. Calculate the correlation between X and Y. Don’t round at intermediate steps. Give your final answer to three decimal places.

D. Interpret the correlation value in the context of this example.

E. Are X and Y independent random variables? How can you tell?

Expert Solution

orchestra answered 3 years ago

Fifteen randomly selected college students were asked to state the number of hours they slept the...

Fifteen randomly selected college students were asked to state the number of hours they slept the previous night. The resulting data are 5, 10, 7, 8, 6, 7, 7, 6, 6, 9, 4, 3, 8, 9, 7. Find the following. (Round your answers to two decimal places.) (a) Variance s2, using formula below $ s^2 = \dfrac{\sum{(x - \overline{x})^2}}{n - 1}$ s2 = (b) Variance s2, using formula $ s^2 = \dfrac{\sum{x^2} - \dfrac{(\sum{x})^2}{n}}{n - 1} $ s2 = (c)...

A study was conducted on the number of hours slept by men and women. A sample...

A study was conducted on the number of hours slept by men and women. A sample of 18 men slept an average of 6.1 hours a day with a sample standard deviation of 2.1 hours, whereas a sample of 21 women slept an average of 6.4 hours a day with a sample standard deviation of 1.7 hours. Use a 0.05 significance level to test the claim that the average number of hours that there is a difference between the average...

The following table shows the weights (in pounds) and the number of hours slept in a...

The following table shows the weights (in pounds) and the number of hours slept in a day by a random sample of infants. Test the claim that Mnot equals≠0. Use alphaαequals=0.10.1. Then interpret the results in the context of the problem. If convenient, use technology to solve the problem. Weight, x 8.28.2 10.110.1 9.99.9 7.17.1 6.96.9 11.111.1 10.910.9 15.115.1 Hours slept, y 14.814.8 14.714.7 14.114.1 14.214.2 13.913.9 13.213.2 13.813.8 12.412.4 1. Identify the null and alternative hypotheses. 2. Calculate the...

(a) The following data shows the number of hours that 8 hospital patients slept following the...

(a) The following data shows the number of hours that 8 hospital patients slept following the administration of a certain anesthetic. 8, 5, 12, 10, 11, 4, 6, 10, Find a 95% confidence interval for the average hours slept following the administration of the anesthetic for the sampled population.

The average number of hours slept per week for college seniors is believed to be about...

The average number of hours slept per week for college seniors is believed to be about 60 hours. A researcher asks 10 random seniors at a University how many hours they sleep per week. Based on the following results, should the researcher conclude that college seniors do or do not sleep an average of 60 hours per week? Data (average number of hours slept per week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55 A: What is the...

Let x be the number of years after 2007 and y represent the number of students...

Let x be the number of years after 2007 and y represent the number of students enrolled at WWCC. Answer the following given the data that enrollment was 2055 in the year 2007, 2244 in 2008, 2512 in 2009, and 2715 in 2010. (a) Find the least-squares line for the data using Excel and submit your file in Canvas. (b) Using partial derivatives, verify the formula you obtained in Excel. (c) Find the least-squares error E.

reconsider dr Sameers research question about how much time cal poly students spend watching tv, and...

reconsider dr Sameers research question about how much time cal poly students spend watching tv, and recall that for random sample of 100 cal poly students number of hours per day spemt watching tv the mean and SD tunred out to be 3.01 hours and 1.97 hours respectively. a. in the context of thios study, is the theory based approach (one sample t-test) valid to find a p value to investigate whether the data provide evidence that the average number...

Let X be the number of students who attend counseling at a certain time of day....

Let X be the number of students who attend counseling at a certain time of day. Suppose that the probability mass function is as follows p (0) = .15, p (1) = .20, p (2) = .30, p (3) = .25, and p (4) = .10. Determine: a) Is this a valid probability mass function? Why? b) Obtain the cumulative probability function c) What is the probability that at least two students come to counseling d) What is the probability...

Let X be the number of heads and let Y be the number of tails in...

Let X be the number of heads and let Y be the number of tails in 6 flips of a fair coin. Show that E(X · Y ) 6= E(X)E(Y ).

A doctor finds that there is a positive correlation between the amount of hours slept and...

A doctor finds that there is a positive correlation between the amount of hours slept and memory performance. What is the best way to show the results? Group of answer choices a.scatterplots b.line graphs c.bar graphs d.pie charts

Question