Anuja is at the bottom left (0, 0) of a coordinate grid of size n ∗ m, and she can only move right and up unit distance along the edges (She cannot move towards the right and above of the point (n, m)). She chooses a path randomly and every path is equally likely. What is the probability that she passes through a point (x, y) in her path? (x>=0 and x<=n and y>=0 and y<=m)

Anuja is at the bottom left (0, 0) of a coordinate grid of size n ∗ m, and she can only move right and up unit distance along the edges (She cannot move towards the right and above of the point (n, m)). She chooses a path randomly and every path is equally likely. What is the probability that she passes through a point (x, y) in her path? (x>=0 and x<=n and y>=0 and y<=m)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

See similar textbooks

Similar questions

1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?
The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.
The height of male students in the school is assumed to be normally distributed. 18% of the students haveheight more than 180 cm and 9% of them have height less than 160 cm. Find µ and σ.
If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?
What is the simple random walk on integers? Does it always return to the origin if p = ½ ? if p ≠ ½?
Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γ E[I], where γ >1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1. [Hint: draw a coordinate plane with p on the x-axis and M on the y-axis.] Based on this graph, under what conditions is she least likely to buy the subsidized insurance?