Choose a point at random in the square with sides 0 <=x≤1 and ≤ y ≤...

Question

Question

Choose a point at random in the square with

sides 0 <=x≤1 and ≤ y ≤ 1. This means that the probability

that the point falls in any region within the square is the area of

that region. Let X be the x coordinate and Y be the

y coordinate of the point chosen. Find the conditional probability Pr(Y<1/3|Y>X).

Hint

Sketch the square and the events

Y<1/3 and Y>X

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the...

Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random: SOME DOGS ARE BROWN (a) Find the probability that the chosen letter is R. (b) Let X denote the length of the chosen word. Determine the probability mass function of X. (c) For each possible value k of X determine the conditional probability P(X k|X 3) Hint. The decomposition idea works...
Let (X, Y ) be a random point in the square {(x, y)| 0 ≤ x,...

Let (X, Y ) be a random point in the square {(x, y)| 0 ≤ x, y ≤ 1}. Compute the density of W = XY , E[W] and Var(W)
2. (a) Die #1 has 6 sides numbered 1, . . . , 6 and die...

2. (a) Die #1 has 6 sides numbered 1, . . . , 6 and die #2 has 8 sides numbered 1, . . . , 8. One of these two dice is chosen at random and rolled 10 times. Find the conditional probability that you have selected die #1 given that precisely three 1’s were rolled. (b) Let X and Y be independent Poisson random variables with mean 1. Are X − Y and X + Y independent? Justify...

3. A point (X, Y) is uniformly distributed on the unit square (0, 1]2. Let 0...

3. A point (X, Y) is uniformly distributed on the unit square (0, 1]2. Let 0 be the angle between the r-axis and the line segment that connects (0,0) to the point (X, Y). Find the expected value El9] (Hint: recall that conin 0 and an
(1 point) Find the length of the curve defined by y=18(8x2−1ln(x))y=18(8x2−1ln⁡(x)) from x=4x=4 to x=8 (1...

(1 point) Find the length of the curve defined by y=18(8x2−1ln(x))y=18(8x2−1ln⁡(x)) from x=4x=4 to x=8 (1 point) Find the area of the region enclosed by the curves: 2y=4x−−√,y=4,2y=4x,y=4, and 2y+1x=52y+1x=5 HINT: Sketch the region! (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=2+1/x4,y=2,x=4,x=9;y=2+1/x4,y=2,x=4,x=9; about the x-axis. (1 point) Find the length of the curve defined by y = $(8x? – 1 In(x)) from x = 4...
5. Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices...

5. Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices (0,0), (2,0),(1,1), (0,1) Uniformly distributed means that the joint probability density function of X and Y is a constant on D (equal to 1/area(D)). (a) Do you think Cov(X, Y) is positive, negative, or zero? Can you answer this without doing any calculations? (b) Compute Cov(X, Y) and pxyCorr(X, Y)

4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) deno...

4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) denote the polar coordinates of the point (X,Y). Find the joint p.d.f. of R and . Compute the covariance between R and 0. Are R and e are independent? (b) Find E(XI{Y > 0}) and E(Y|{Y > 0}) (c) Compute the covariance between X and Y, Cov(X,Y). Are X and Y are independent? 4. A random...
3. Let X be an exponential random variable with parameter 1 = $ > 0, (s...

3. Let X be an exponential random variable with parameter 1 = $ > 0, (s is a constant) and let y be an exponential random variable with parameter 1 = X. (a) Give the conditional probability density function of Y given X = x. (b) Determine ElYX]. (c) Find the probability density function of Y.
A square loop with sides of length L lies in the x-y plane in a region...

A square loop with sides of length L lies in the x-y plane in a region in which the magnetic field points in the z-direction and change over time as B(t)=B0e^(-5t/t0)k. Find the magnitude of the EMF induced in the wire, show the direction of the induced current in the loop using Lenz's law. A square loop with sides of length L lies in the r-y plane in a region in which the magnetic field points in the z-direction and...

Problem 3 Let A be a "random point" that coincides with the point a1,a2,as or as...

Problem 3 Let A be a "random point" that coincides with the point a1,a2,as or as with equal probabil- ities. d4 Let a random variable X be the first coordinate of the point A, a random variable Y be the scond coordinate of the point A. (a) Find the joint distribution of random variables X and yY (b) Find the marginal distribution of X and Y. (c) Find the cumulative distribution functions of X and Y (d) Compute E(X] and...