Consider the triangle with vertices (0, 0), (1, 0), (0, 1). Suppose that (X, Y) is a uniformly chosen random point from this triangle. (a) Sketch the support of joint distribution (X, Y). (b) Find the marginal density functions of X and Y. (c) Calculate the expectations E[X] and E[Y]. (d) Calculate the expectation E[XY]. (e) Determine whether X and Y are independent.

17. a researcher measures three variables, x, y, and z for each individual in a sample of n = 20. the pearson correlations for this sample are rxy = 0.6, rxz = 0.4, and ryz = 0.7. a. find the partial correlation between x and y, holding z constant. b. find the partial correlation between x and z, holding y constant. (hint: simply switch the labels for the variables y and z to correspond with the labels in the equation.) gravetter, frederick j. statistics for the behavioral sciences (p. 526). cengage learning. kindle edition.

Jose is going to use a random number generator 500500 times. each time he uses it, he will get a 1, 2, 3,1,2,3, or 44.

Of f(x) is byof f(x)=-3|x| x-.f(x)? a )f(x)=3|x| b) f(x)=|x+3| c) f(x)= -3|x| d) f(x)= -|x+3|