On a line segment AB of length l, two points C and D are placed at random and independently. What is the probability that C is closer to D than to A?
PS I understand that the marginal pdfs are f = 1/l, but how can I find the joint pdf?
On a line segment AB of length l, two points C and D are placed at...
4. A point, A, is chosen at random with uniform distribution on a line segment of length L. A second point, B, is chosen randomly, independently of the first one. Find the probability that B is closer to A than to either of the two endpoints of the line segment.
Question 1 (1 point) A line segment AD, contains points B & C such that C is between A and D, and B is between A and C. If AB- 6, BD- 23, and AB -CD, find the length of segment BC. 17 23 29 Not enough information to solve the problem
Two points are chosen randomly in a segment line of length . Prove that the probability that the distance between such points to be less than is , where is a defined distance before doing the experiment and . Any help will be appreciated, thanks
5 (10 points). We start with a stick of length L. Break it at a point cho sen uniformly randomly and keep the piece that contains the left end. Let its length be Y. Repeat the same process on this stick with length Y. Let X be the length of the remaining piece. a) (2 points) Find the joint PDF of X and Y b) (3 points) Find the marginal PDF of X c) (3 points) Use the PDF of...
A point is chosen at random on a line segment of length 12. Find the probability that the ratio of the shorter to the longer segment is less than 3/20.
2. Let Xi and X2 be two continuous random variables having the joint probability density 1X2 , for 0, elsewhere. If Y-X? and Y XX find a. the joint pdf of Yǐ and Y, g(n,n), b. the P(Y> Y), c, the marginal pdfs gi (m) and 92(h), d. the conditional pdf h(galn), and e, the E(YSM-m) and E(%)Yi = 1/2).
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.
Let Xi and X2 be two continuous random variables having the joint probability density f,2)10 0, elsewhere. a. the joint pdf o1% and Y2.9(Y1,Y2), b, the P06 > Yi), c. the marginal pdfs gn () and g2(2), d. the conditional pdf h(walvi), and e. the E(Yalki-y) and E(gYi = 1/2).
(7 points) Suppose X and Y are continuous random variables such that the pdf is f(x,y) xy with 0 sx s 1,0 s ys 1. a) Draw a graph that illustrates the domain of this pdf. b) Find the marginal pdfs of X and Y c) Compute μΧ, lly, σ' , σ' , Cov(X,Y),and ρ d) Determine the equation of the least squares regression line and draw it on your graph. (7 points) Suppose X and Y are continuous random...
Two points are selected randomly on a line of length 1, as X and Y as shown in the figure. Therefore X is the smaller of the two points and Y is the larger of the two points. Y 1 (i) Find the joint probability density function of X and Y. (ii) What is the expected length E(Y – X)?