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Two points are selected randomly on a line of length 1, as X and Y as...
(1 point) Two points are selected randomly on a line of length 16 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distriuted over [0,8) and Y is uniformly distributed over (8,16] Find the probability that the distance between the two points is greater than 6. P(|X – Y| > 6) =
(1 point) Two points are selected randomly on a line of length 10 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over [0,5) and Y is uniformly distributed over (5, 10]. Find the probability that the distance between the two points is greater than 2. answer:
7. A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the pro- portion of time that the second line is in use. Suppose that the joint probability density function for (X,Y) is f(tv) = ( +y), if 0 <r,y<1. elsewhere. (a) Compute the probability that neither line is busy more than half the time. (b) Determine whether or not...
Problem 5. Two points are selected independently and randomly on a line of length 15 inches so as to be on opposite sides of the midpoint of the line. Find the probability that the distance between the two points is greater than 5 inches.
Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (b) Compute E(X) and the conditional expectation E(X|Y= 1).
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
(1 point) Two points along a straight stick of length 49 cm are randomly selected. The stick is then broken at those two points. Find the probability that all of the resulting pieces have lenght at least 7.5 cm. probability =
(1 point) Two points along a straight stick of length 38 cm are randomly selected. The stick is then broken at those two points. Find the probability that all of the resulting pieces have lenght at least 4.5 cm. probability =