(1 point) Two points are selected randomly on a line of length 16 so as to...
(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:
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.
Please be clear and show all steps. Please specify how to get f(x) and f(y) and also specify how to get the limits of the integration. i will give it a LIKE. Thank you. Two points are selected randomly on a line of length L so as to be on opposite sides of the mid- point of the line. [In other words, the two points X and Y are independent random variables such that X is uniformly distributed over (0,...
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)?
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the longer piece is less than 1/4. 3 marks (b) Suppose X1 and X2 are two iid normal N(μ, σ*) variables. Define Are random variables V and W independent? Mathematically justify your answer 3 marks (c) Let C denote the unit circle...
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the longer piece is less than 1/4 3 marks (b) Suppose X, and X2 are two iid normal N(μ, σ2) variables. Define Are random variables V and W independent? Mathematically justify your answer. 3 marks] (c) Let C denote the unit circle...
(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 =
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
A stick is broken into three pieces at two randomly chosen points on the stick. What is the probability that no piece is longer than half the length of the stick? To do this problem, it is useful to split it into the following steps (assuming the length of stick is 1). (a) Let U1 and U2 are independent and uniformly distributed on (0, 1). Define X = min(U1, U2) and Y = max(U1, U2). Use the fact that P(a...