Consider two random variables X and Y with joint PMF given in the following Tablex= Number of Bars of SignalStrength123y= Response10.010.020.25time(nearest second)20.020.030.203 0.020.100.0540.150.100.05a) Find P(X = 1, Y≤3)b) Find the marginal PMFs of X and Y.c) Find P(Y=1|X=1)d) Are X and Y independent?e) For the discrete random variables X and Y, Find E(Y|X=1) and V(Y|X=1)?

Answered: Image /qna-images/answer/1f505c80-3dd6-4872-b791-c367f059bf90.jpg

Answered: Consider two random variables X and Y…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A random variable X obeys Exponential(λ) distribution. Suppose X has 100 samples Xi, i = 1, 2, ··· , 100. If M100(X)=3.5, please determine an interval estimation of λ with confidence level β = 96%.
Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. We would like to test Ho : µ = µo versus H1 : µ + µo. What test statistic should you should use to test Ho versus H1? Select one: X- O a. Z= N(0, 1) O b. T = tn-1 O c. W = (n-1)s2 Xn-1 Now suppose that n = 16, the observed sample mean a is 8.9. the observed sample variance s is 25 and Ho = 10.5. Suppose we next want to compute a 95% confidence interval for u. What is the lower endpoint of this 95% confidence interval? Give answer to three decimal places. What is the upper endpoint of this 95% confidence interval? Give answer to three decimal places.
Our method of calculating a 95 percent confidence interval for the mean µ of a normal population, with known variance o2, is 1.960 1.960 Xn Xn + This method of creating an interval has the property that a single SRS of size n will provide an interval that will containing u with 0.95 probability. If five different individuals select 5 independent samples, each of size their resulting five interval estimates of 4, (i) what is the probability that u will belong to all five of them: (ii) None will contain µ? (iii) What is the probability that at least one of the intervals will contain u? and obtain п, The following``answers" have been proposed. (a) (i) (0.95)5, (ii) (0.95)5, (iii) (0.95)5. (b) (i) (0.05)5, (ii) 1– (0.05)5, (iii) (0.95)5, (c) (i) 1 – (0.05)5, (ii) (0.05)5, (iii) (0.95)5. (d) (i) (0.95)5, (ii) (0.05)5, (iii) 1 – (0.05)5. (e) None of the above. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The sample mean was 15.1 with sample standard deviation s = 2.51. Does this information indicate that the population average HC for this patient is higher than 14? Use α= 0.05.
A researcher investigates whether or not a new cold medication affects mental alertness. A standardized test of alertness is normally distributed with μ = 64 and σ = 8. A random sample of n = 16 students are given the new cold medication and are asked to take the standardized test of alertness. For the sample of n = 16 students, the mean score on the test M = 58. Using the 7 steps of hypothesis testing determine if the new cold medication affects mental alertness (i.e., there is a difference in mental alertness with the cold medication) using α = .05 For this problem 5. Do your statistical calculations 6. Make your decision
5. An hypothesis test is of the form Ho : µ1 – Hz = 0 vs Ha : µ1 – H2 < 0. Both populations are assumed normal with equal variance and samples are assumed independent. We draw 21 observations for the first sample and 37 observations for the second sample. State the distribution of the test statistic for this test. t-distribution with 60 degrees of freedom t-distribution with 58 degrees of freedom) Normal distribution with 57 degrees of freedom O t-distribution with 56 degrees of freedom
Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2. Consider independent random samples, Ya, Y2. the ith population with sample mean Y, and sample variance S² = Yin, of size n,, from (Y-₁². (a) What is the distribution of Y,? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho : 4 = o versus Ha i Pio when of is unknown and n, is small. : (e) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
A researcher calculates a sample correlation of -0.8 from a sample of size 13. He wants to conduct a hypothesis test in order to determine if the population correlation is less than 0. What is the value of the test statistic? Round your final answer to three decimals and enter it in the first blank. What is the critical value cutoff for the rejection region? Use a value of alpha and enter your answer in the second blank. Your critical value should include 3 decimals. = 0.1 Blank # 1 Blank # 2
A researcher investigates whether or not a new cold medication affects mental alertness. A standardized test of alertness is normally distributed with μ = 64 and σ = 8. A random sample of n = 16 students are given the new cold medication and are asked to take the standardized test of alertness. For the sample of n = 16 students, the mean score on the test M = 58. Using the 7 steps of hypothesis testing determine if the new cold medication affects mental alertness (i.e., there is a difference in mental alertness with the cold medication) using α = .05 For this problem 1. State the hypothesis in words 2. State the statistical hypothesis (H1 and Ho) 3. State the α level = 4. State the decision rule and be sure to include the critical value
Let µj and µz represent the population means and let "= 2 A test will be made of the hypotheses Ho "a=0 versus 41 "a>0. Can you reject Ho at the a= 0.05 level of significance?
For the hypothesis test Ho :µ = 16 against Hj : µ < 16 with variance unknown and n = 10, find the best approximation for the P-value for the test statistic to = 1.968. O 0.950
A research study investigated the composition of wines from the Rhine and Moselle wine regionsof Germany. One component measured was the concentration of i-Butyl alcohol. The results ofthe study are listed in the following table:Region n i-Butyl alcohol (mg/100ml)Rhine 9 ̄x =5.32,s =2.24Moselle 14 ̄x =3.62,s =0.97(a) Assume that the underlying population variances from the two regions are identical. At the0.05 level of significance, test the null hypothesis that the mean concentration of i-Butylalcohol is the same for wines from the Rhine and Moselle regions.Construct a 95% confidence interval(b) Now assume that the underlying population variances from the two regions differ. At the 0.05level of significance, test the null hypothesis that the mean concentration of i-Butyl alcohol isthe same for wines from the Rhine and Moselle regions, construct a 95% confidence interval(c) If you were to provide a report to the investigators which of the above results would youinclude and why?

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS