Task 1 At a hospital, the analysis department uses Monte Carlo simulations to plan operations during a pandemic. In the questions below, it can be assumed that the Monte Carlo model used gives a correct picture of how the pandemic will behave in the future. In this assignment we have access to 100,000 independent simulations from the random variable X, which is defined as the number. intensive care beds that will be in use on a given day in the future by patients who have become ill as a result. of the pandemic. These simulations are given in the R-vector beds. Below is a histogram of the contents of beds: Ang number of intensive care beds in use Here are the results of some R commands applied to beds: > beds [1:5] # print first 5 values [1] 2 4 1 3 5 > summary (beds) Min. 1st Qu. Median 0.000 2.000 3.000 > quantile (beds, probs=c 2.5% 5% 95% 97.5% 1 1 5 6 > sd (beds) [1] 1.372583 > sum (beds ==0) [1] 166 Max. 15.000 Mean 3rd Qu. 3.002 4.000 (0.025,0.05,0.95,0.975)) 1.) What is the estimate for the expected number of intensive care beds in use on the given day? 2.) How many beds must be available to be 95% sure of having enough beds? 3.) Estimate the probability that no intensive care beds are in use on the given day.
Task 1 At a hospital, the analysis department uses Monte Carlo simulations to plan operations during a pandemic. In the questions below, it can be assumed that the Monte Carlo model used gives a correct picture of how the pandemic will behave in the future. In this assignment we have access to 100,000 independent simulations from the random variable X, which is defined as the number. intensive care beds that will be in use on a given day in the future by patients who have become ill as a result. of the pandemic. These simulations are given in the R-vector beds. Below is a histogram of the contents of beds: Ang number of intensive care beds in use Here are the results of some R commands applied to beds: > beds [1:5] # print first 5 values [1] 2 4 1 3 5 > summary (beds) Min. 1st Qu. Median 0.000 2.000 3.000 > quantile (beds, probs=c 2.5% 5% 95% 97.5% 1 1 5 6 > sd (beds) [1] 1.372583 > sum (beds ==0) [1] 166 Max. 15.000 Mean 3rd Qu. 3.002 4.000 (0.025,0.05,0.95,0.975)) 1.) What is the estimate for the expected number of intensive care beds in use on the given day? 2.) How many beds must be available to be 95% sure of having enough beds? 3.) Estimate the probability that no intensive care beds are in use on the given day.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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![Task 1
At a hospital, the analysis department uses Monte Carlo simulations to plan operations
during a pandemic. In the questions below, it can be assumed that the Monte Carlo model
used gives a correct picture of how the pandemic will behave in the future. In this assignment
we have access to
100,000 independent simulations from the random variable X, which is defined as the
number.
intensive care beds that will be in use on a given day in the future by patients who have
become ill as a result.
of the pandemic. These simulations are given in the R-vector beds. Below is a histogram of
the contents of beds:
5
8
20
0.00
number of intensive care beds in use
Here are the results of some R commands applied to beds:
> beds [1:5] # print first 5 values
[1] 2 4 1 3 5
> summary (beds)
Min. 1st Qu.
0.000
Mean 3rd Qu.
3.002
4.000
(0.025,0.05,0.95,0.975))
Median
2.000 3.000
> quantile (beds, probs=c
2.5% 5% 95% 97.5%
1
1
5 6
> sd (beds)
[1] 1.372583
> sum (beds==0)
[1] 166
Max.
15.000
1.) What is the estimate for the expected number of intensive care beds in use on the given day?
2.) How many beds must be available to be 95% sure of having enough beds?
3.) Estimate the probability that no intensive care beds are in use on the given day.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1eb473a3-5d78-4231-b18a-73cbb766f295%2F3547b6c4-4f55-44f5-863c-5f65c7e3bc02%2F3tgxrtc_processed.png&w=3840&q=75)
Transcribed Image Text:Task 1
At a hospital, the analysis department uses Monte Carlo simulations to plan operations
during a pandemic. In the questions below, it can be assumed that the Monte Carlo model
used gives a correct picture of how the pandemic will behave in the future. In this assignment
we have access to
100,000 independent simulations from the random variable X, which is defined as the
number.
intensive care beds that will be in use on a given day in the future by patients who have
become ill as a result.
of the pandemic. These simulations are given in the R-vector beds. Below is a histogram of
the contents of beds:
5
8
20
0.00
number of intensive care beds in use
Here are the results of some R commands applied to beds:
> beds [1:5] # print first 5 values
[1] 2 4 1 3 5
> summary (beds)
Min. 1st Qu.
0.000
Mean 3rd Qu.
3.002
4.000
(0.025,0.05,0.95,0.975))
Median
2.000 3.000
> quantile (beds, probs=c
2.5% 5% 95% 97.5%
1
1
5 6
> sd (beds)
[1] 1.372583
> sum (beds==0)
[1] 166
Max.
15.000
1.) What is the estimate for the expected number of intensive care beds in use on the given day?
2.) How many beds must be available to be 95% sure of having enough beds?
3.) Estimate the probability that no intensive care beds are in use on the given day.
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