Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professionalbasketball player makes in a season. A random sample of n =6 professional basketball players gave the following information.676475867373444148514451(a) Verify that Ex438, Ey = 279, Ex = 32264, Ey = 13059, Exy = 20493, and r 0.800.%3D%3DΣχEyEx?Σχy(b) Use a 5% level of significance to test the claim that p > 0. (Round your answers to two decimal places.)critical tConclusionReject the null hypothesis, there is sufficient evidence that p > 0.Reject the null hypothesis, there is insufficient evidence that p > 0.Fail to reject the null hypothesis, there is insufficient evidence that p > 0.Fail to reject the null hypothesis, there is sufficient evidence that p > 0.(c) Verify that S 2.7729, a 14.783, b - 0.4345, and x 73.000.eSela(d) Find the predicted percentage ŷ of successful field goals for a player with x = 71% successful free throws. (Round your answer to two decimal places.)%(e) Find a 90% confidence interval for y when x = 71. (Round your answers to one decimal place.)lower limit%upper limit(f) Use a 5% level of significance to test the claim that B > 0. (Round your answers to two decimal places.)criticalConclusion

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1=(X1/r1)/(X2/r2) and Y2=X2. (a) Find the joint pdf of Y1 and Y2.
Let Z be a standard normal random variable. Determine the value of c. P(0.55 is less than or equal to Z is less than or equal to c)=0.2773 Carry intermediate computations to at least 4 decimal places. Round answer to 2 decimal places.
Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1 Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. (d) Find the predicted percentage of strikeouts for a player with an x = 0.35 batting average. (Use 2 decimal places.)%(e) Find a 95% confidence interval for y when x = 0.35. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 1% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t critical t ±
Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1 Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. (e) Find a 95% confidence interval for y when x = 0.35. (Use 2 decimal places.) lower limit % upper limit (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit
Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1 Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit
Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c . =P≤c≤Z−0.540.2810 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Let Z be a standard normal random variable. Determine the value. P(Z is less than or equal to c)=0.8621 Carry intermediate computations to at least 4 decimal places. Round answer to 2 decimal places.
Let Y be a discrete random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2
Indicate the range of values that the random variable X may assume and classify the random variable as finite/infinite and continuous/ discrete in the following experiments. I. The wait time in minutes until a bus arrive at the bus stop. II. The duration of a telephone conservation
Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.338 0.306 0.340 0.248 0.367 0.269 y 3.5 7.7 4.0 8.6 3.1 11.1 Σx = 1.868, Σy = 38, Σx2 = 0.592034, Σy2 = 294.32, Σxy = 11.1556, and r ≈ -0.901. Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t critical t ± Conclusion Reject the null hypothesis, there is sufficient evidence that ρ differs from 0. Reject the null hypothesis, there is insufficient evidence that ρ differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ differs from 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ differs from 0.
Let X be a discrete random variable with PMF Px(X) = { (0.5, x=2) (0.3, x=5) (0.2, x=6) (0, otherwise) a. Find, and graph, the CDF for this random variable. b. Find the expected value, EX . c. Find the variance, Var(X ). d. Let y = 5/x Find the expected value EY.
Consider the continuous random variable x, which has a uniform distribution over the interval from 10 to 15. The probability that x will take on a value of at least 13 is

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