A group of n people get on an elevator at Floor 0. There are m floors...

A group of n people get on an elevator at Floor 0. There are m floors besides Floor 0. Each person uniformly randomly chooses one of those m floors to stop at. (All choices are independent, and no one gets on the elevator after Floor 0.) The elevator stops at a floor if at least one person has chosen to stop there. Let X be the number of stops that the elevator makes after Floor 0.

(a) What is E[X]? Var(X)?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

We have n people and K floors: what is the chance that 1)all people get off...

We have n people and K floors: what is the chance that 1)all people get off in the smae floor? 2)at least one in evey floor?3)P( floor 3 is empty)?4)p(2 people get out in the first floor and 3 people or mpre get off in the second floor)

Seven people are in an elevator which stops at ten floors. In how many ways can...

Seven people are in an elevator which stops at ten floors. In how many ways can they get off the elevator? 10^7 C(10,7) 7^10 P(10,7) A hiking group consists of 12 students and 2 leaders. A leader must be at the front and back of the line. How many ways can the group hike in a line? 14! 12!*2! 14!/2! 12!

A box of mass M sits on the floor of an elevator at rest. Gravity (which...

A box of mass M sits on the floor of an elevator at rest. Gravity (which has a strength set by the local acceleration due to gravity g) pulls the box and the floor pushes the box. The net or total force on the box is zero. What is the force on the box from the floor? Give both the magnitude and the direction. Now imagine that the elevator is accelerating upwards at acceleration a. Now the two forces on...

A team of size m has to be chosen from a group of n people (m...

A team of size m has to be chosen from a group of n people (m < n) and a captain chosen for the team. (a) How many ways can the captained team be chosen if the captain is chosen first then the remainder of the team chosen. (b) How many ways can the captained team be chosen if the team is chosen first then the captain chosen from the team? This should give the same number as a) but...

Five people on the basement of a building get on an elevator that stops at seven...

Five people on the basement of a building get on an elevator that stops at seven floors. Assuming that each has an equal probability of going to any floor, find (a) the probability that they all get off at different floors; (3 POINTS) (b) the probability that two people get off at the same floor and all others get off at different floors. (4 POINTS)

Five people on the basement of a building get on an elevator that stops at seven...

Five people on the basement of a building get on an elevator that stops at seven floors. Assuming that each has an equal probability of going to any floor, find (a) the probability that they all get off at different floors (b) the probability that two people get off at the same floor and all others get off at different floors.

Let function F(n, m) outputs n if m = 0 and F(n, m − 1) +...

Let function F(n, m) outputs n if m = 0 and F(n, m − 1) + 1 otherwise. 1. Evaluate F(10, 6). 2. Write a recursion of the running time and solve it . 3. What does F(n, m) compute? Express it in terms of n and m.

A monkey sits on a bathroom scale which is on the floor of an elevator for...

A monkey sits on a bathroom scale which is on the floor of an elevator for a very tall building. The monkey has a mass of 42.0 kg. What is the reading on the scale if there is not motion and no acceleration? When the elevator starts moving the scale reads 480 N. Describe the acceleration for this case. At another time the scale reads 360 N. Describe the acceleration for this second case. Calculate the acceleration in each...

1) a. There is an elevator on the 102th floor of the Empire State Building with...

1) a. There is an elevator on the 102th floor of the Empire State Building with a sign: MAXIMUM WEIGHT 2900 LBS. During refurbishment, the cable was being replaced. A section of the new cable is cut up and tested for its breaking strength. The cable was tested 20 times and the average breaking point of the sample was found to be 3100 LBS with a standard deviation of 280 LBS. Construct an appropriate hypothesis test that determines whether the...

An object is placed on the floor of an elevator. Which of the following statements is...

An object is placed on the floor of an elevator. Which of the following statements is correct regarding the magnitude of the normal force that the elevator floor exerts on the object? A) It is always the same as the weight of the object regardless the state of motion of the elevator B) It is less than the weight of the object if the elevator moves downward with a constant velocity C) It is largest if the elevator undergoes free...

Subjects