(1 point) Two points along a straight stick of length 49 cm are randomly selected. The...
(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 =
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(1 point) Two points along a straight stick of length 49 cm are
randomly selected. The...
(1 point) Two points along a straight stick of length 38 cm are randomly selected. The...
(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 =
A stick of length one is broken into two pieces at a random point. What is...
A stick of length one is broken into two pieces at a random point. What is the probability that the length of the longer piece will be at least three times the length of the shorter piece?
A stick is broken into three pieces at two randomly chosen points on the stick. What is the proba...
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...
Suppose that a point is chosen at random on a stick of unit length and that the stick is broken into two pieces at that point. Then, we form a right angle with two pieces of stick, forming the two sho...
Suppose that a point is chosen at random on a stick of unit length and that the stick is broken into two pieces at that point. Then, we form a right angle with two pieces of stick, forming the two shorter sides of a right-angled triangle. Let Θ be the smallest angle in this triangle. Define Y = tanΘ and W = cotΘ. Find E(Y ) and the p.d.f of W.
(1 point) Two points are selected randomly on a line of length 10 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:
(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 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) =
A stick of length L is broken in two pieces at a point which is uniformly...
A stick of length L is broken in two pieces at a point which is uniformly distributed on the stick’s length. What is the expectation of the ratio of the smaller length to the larger?
Two points are selected randomly on a line of length 1, as X and Y as...
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)?
Problem 5. Two points are selected independently and randomly on a line of length 15 inches...
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.
5 (10 points). We start with a stick of length L. Break it at a point...
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...
(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 =
A stick of length one is broken into two pieces at a random point. What is the probability that the length of the longer piece will be at least three times the length of the shorter piece?
(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:
(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) =
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)?
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.
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...
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