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Ainat [17]
3 years ago
13

A group of n people enter an elevator in a building with k floors. Each person independently selects a floor uniformly at random

(each with equal probability 1/k). The elevator stops at each floor selected (by at least one person). Let N be the number of stops. (a) [3 marks] Find a simple expression for EN, the average number of stops. Bonus [2 marks] Suppose that n
Mathematics
1 answer:
____ [38]3 years ago
4 0

Answer:

Hence the person stop at floor by at least one person will be

E(X)=(summation from K=1 to k)[1-{(k-1)/k}^n]

Step-by-step explanation:

Given:

There are n peoples and k floors in a building.

Selects floor with 1/k probability .

To find :

Elevator stop at each floor by at least one person.

Solution:

Now

let K= number of floor at which at least one person will be stopping.

For getting E(X)

consider a variable Ak =1 if a least one person get of the elevator

and values for k=1,2,3.....k

K=(summation From k=1 to k)Ak

E(K)=((summation From k=1 to k) E[Ak]

=(summation From k=1 to k)[1-{(k-1/k)^n

Hence the person stop at floor by at least one person will be

E(K)=(summation from K=1 to k)[1-{(k-1)/k}^n]

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A rectangular carpet has a perimeter of 274 inches. The length of the carpet is 95 inches more than the width. What are the dime
GrogVix [38]

Answer:

Length: 116

Width: 21

Step-by-step explanation:

Let's say that the width of carpet is x. If the length of the carpet is 95 inches more than the width, then let's say that the width is x + 95.

Since we are solving for the perimeter, you have to multiply the width and the length(x and x + 95) by two.

So,

2x + 2x + 190 = 274.

Simplify this and you get:

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So, the width is 21. This means that the length is 21 + 95.

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Step-by-step explanation:

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Answer:

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256π/3 cm³

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<u>Step 1</u>

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<u>Step 2</u>

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<u></u>

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