Let X and Y be two independent random variables such that E[X]=3, E(Y)=4, V(X)=10 and V(Y)=20. Then E(X – Y)²] is equal to: а. 55 b. 31 с. 20 d. 15
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- 54% of all the town's residents own a dog and 65% own a cat. Of the dog owners 45% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible) а. Р(Own a Dog) b. P(Own a Cat) = c. P(Own a Cat and a Dog) = d. P(Own a Dog GIVEN Own a Cat) =A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99Are Republicans less likely than Democrats to display the American flag in front of their residence on the Fourth of July? 409 of the 660 Republicans surveyed display the flag on the Fourth of July and 472 of the 687 Democrats surveyed display the flag on the Fourth of July. What can be concluded at the a = 0.05 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer v Select an ahswer vSelect an answer v (please enter a decimal) H1: [Select an answer Select an answer v Select an answer v (Please enter a decimal) b. The test statistic ? v (please show your answer to 3 decimal places.) !! c. The p-value (Please show your answer to 4 decimal places.) d. The p-value is ? va e. Based on this, we should Select an answer v the null hypothesis.
- 4. Let X - N(u, o²). The characteristic function (ch.f.) of X is given by $(w) = ejHw-o?w?/2, W E R, where j = v-1 is the imaginary unit. Use the ch.f. to find the mean and variance of X.2. Let X and Y be independent random variables with E[X] = 4, Var[X] = 84, E[Y] = 6, and Var[Y] = 54. Find E[5X + 2Y - 18] - b. Find E[-3Y+X+3] -a. -с. Find E[X2] d. Find ox e. Find E[Y2] f. Find Oy g. Find Var[X+3Y - 6] h. Find Var[3X - 2Y + 35] Find E[(2X - 8)/5] j. Find Var[(2X - 8)/5] i.need correctly
- Suppose that X and Y are random variables with E(X) = 1, E(X²) = 5, E(Y) = 3, and E(XY) = 1. Match up the following quantities. Cov(X,Y) Corr(X, Y) Var(-X/2) Cov(X/2,-2Y + 3) Drag answer here Cannot be determined Drag answer here Drag answer here 2 Cannot be determined 1. Let X and Y be random variables and let AE B. Prove that the function X(w), if we A, Y(w). if w€ AC is a random variable. Z(w) =We have the following information about the random variables X and Y: 4 8 11 4 5 ox = o Cov(X, Y) 225 15 75 225 Calculate the standard deviation of Z 3Y — Х. oz
- The proportion of students who get an undergraduate degree in statistics in four years was compared for meals and females. Random sample of 200 male statistics majors and 200 female statistics majors were taken. Choose the appropriate parameter(s) for this situation. [Hint: The .parameter(s) to be used in your hypothesis] ule u 2.00 jo None of these .A O P1-P2.B O H.C O Hi- H2.D O P.E O إنهاء المحاولة . . . PREVIOUS ACTIVITY Note P Type here to search Ae Ps 近Answer accurately.For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) = c, Find: а. Var(3X — 5Y). b. The correlation coefficient between X and Y, p. The range of values of c for which the assumptions of the problem are consistent. С.