X and Y are two discrete random variables that are jointly distributed according to the following joint p.m.f. 5 10 X 20 50 0.2 0.2 0.2 10 0.1 0 0.3 Find the correlation coefficient of X and Y. O a. -0.3 O b. -0.15 O c. 0 O d. 0.15 O e. 0.3
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- Which of the following random variables is discrete? a. W=duration of travel (in minutes) from house to school b. X = proportion of failing subjects of a student in a semester c. Y = number of business permits issued each month in Makati d. Z = weight of dog food (in kilograms) supplied by a certain pet store per monthCassie is a gym teacher who develops a training regimen to promote physical health among elementary school students. She knows that scores on a measure of physical health are normally distributed with µ = 75 and σ = 10. She randomly selects one student in her class to complete the training regimen, and this students scores X = 82 on the measure of physical health afterwards. Based on this score, Cassie can conclude that the training regimen _____. A. does have an effect on physical health because this score or larger would be expected 75.80% of the time even if the training regimen does not have an effect. B. does have an effect on physical health because this score or larger would be expected 24.20% of the time even if the training regimen does not have an effect. C. does not have an effect on physical health because this score or larger would be expected 24.20% of the time even if the training regimen does not have an effect. D. does not have an…Consider the following joint random variable pmf for X and Y: x y -1 0 1/4 0 1 1/8 1 1 1/2 1 0 1/8 What is the correlation of X and Y?
- Assume the following data displays the joint probability for random variables X and Y: X 10 20 30 20 0.1 0.2 0.05 0.05 0.1 0.2 0.2 0.0 0.1 -1 Y O 1 1. Solve for the correlation of X and Y. 2. Solve for the correlation of X and Y conditional on Y being greater than or equal to zero. 3. Are X and Y independent? Are X and Y conditional on Y being greater than or equal to zero, independent.2Let the random variables X and Y have the joint p.m.f. x+ y f (x, y) = 32 x = 1, 2, y = 1,2,3,4. Find the means lx and uy, the variances oy and oý, and the correlation coefficient p. Are X and Y independent or dependent? 6.
- For a sample of n = 25 individuals, how large a Pearson correlation between two variables, X and Y, is necessary to be statistically significant for a two-tailed test with α = .05? A)0.405 B)0.382 C)0.389 D)0.397The scatterplot below shows the relationship between two random variables X and Y. (a) Is the correlation a good metric for describing the relationship between X and Y for these data? Why or why not? Regardless of your answer suppose you calculated the sample correlation between X and Y and found that r = -0.15. Explain in one sentence what this means. (b) If, as noted in (a), r = -0.15 then what is the value of the correlation between 2X and 5Y? (c) Based on (b) draw your best approximation to the least squares regression line that fits the data above. Also, make a rough sketch of the corresponding residual plot.Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance a. Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance b. multiplied by the product of the standard deviations for x and y. c. multiplied by the standard deviation of y and divided by the standard deviation of x. d. multiplied by the standard deviation of x and divided by the standard deviation of y.
- We have the following information regarding the random variables X, X, and X3: Var(X1) = Var(X2) = Var(X3), Px, X2 = 0.2, pxX, = 0.5, px X Calculate the correlation between X+ X3 and X2 + X3. (i.e. calculate px+Xs.X2+X3) 0.9. %3DLet X have beta distribution with a = 2 and B = 3. Then the mean and the variance of X, respectively, are Select one: O a. 0.04 and 0.4 O b. 0.02 and 0.04 O c. 0.4 and 0.04 O d. 0.4 and 0.20