Nurses at the ER noticed that patients arrive to the hospital at a rate of 5 individuals per hour, and the time between patient arrivals was Exponentially distributed. Let X = the time between patient arrivals at the ER. Figure 3.1: The probability density function of the time between patient arrivals. 00 20 In addition, recall the R commands related to an exponential distribution mentioned in the pre-reading exp( x, rate), where pexp: CDF function: F(x) = P(X s x) dexp: PDF function. rexp: Random draws from an Exponential distribution. qexp: Gives the quantile function. Let's find some probabilities and quantiles: 1. Find the probability that the time between patient arrivals is a. 30 minutes or less. b. Between 30 minutes and one hour. c. At least one hour. [Hint: An expression for a probability can look like one of the following: P(a < x < b), P(a s X ), P(a s x < b), P(a < X), P(a s X), P(X > b), P(X 2 b), etc.] 2. Find the first quartile, median, and third quartile of X. That is, find a value q, such that F(q) = P(X < q) = 0.25, 0.5 and 0.75.
Nurses at the ER noticed that patients arrive to the hospital at a rate of 5 individuals per hour, and the time between patient arrivals was Exponentially distributed. Let X = the time between patient arrivals at the ER. Figure 3.1: The probability density function of the time between patient arrivals. 00 20 In addition, recall the R commands related to an exponential distribution mentioned in the pre-reading exp( x, rate), where pexp: CDF function: F(x) = P(X s x) dexp: PDF function. rexp: Random draws from an Exponential distribution. qexp: Gives the quantile function. Let's find some probabilities and quantiles: 1. Find the probability that the time between patient arrivals is a. 30 minutes or less. b. Between 30 minutes and one hour. c. At least one hour. [Hint: An expression for a probability can look like one of the following: P(a < x < b), P(a s X ), P(a s x < b), P(a < X), P(a s X), P(X > b), P(X 2 b), etc.] 2. Find the first quartile, median, and third quartile of X. That is, find a value q, such that F(q) = P(X < q) = 0.25, 0.5 and 0.75.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Nurses at the ER noticed that patients arrive to the hospital at a rate of 5 individuals per hour,
and the time between patient arrivals was Exponentially distributed.
Let X = the time between patient arrivals at the ER.
Figure 3.1: The probability density function of the time between patient arrivals.
4.
2.
00
0.5
10
1.5
20
In addition, recall the R commands related to an exponential distribution mentioned in the pre-reading:
<d, p, q, r>exp( x, rate),
where
рехр:
CDF function: F(x) = P(X sx)
dexp:
PDF function.
rexp:
Random draws from an Exponential distribution,
:dxeb
Gives the quantile function.
Let's find some probabilities and quantiles:
1. Find the probability that the time between patient arrivals is
a. 30 minutes or less.
b. Between 30 minutes and one hour.
c. At least one hour.
[Hint: An expression for a probability can look like one of the following:
P(a < x < b), P(a sXs b), P(a s X < b), P(a < X), P(a s X), P(X > b), P(X 2 b), etc.]
2. Find the first quartile, median, and third quartile of X. That is, find a value q, such that
F(q) = P(X <q) = 0.25, 0.5 and 0.75.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11975913-217e-4623-a35d-1e2231fefb08%2F0e940b12-619b-4f4b-b7ab-e9cf458464b6%2Fif8y3ou_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Nurses at the ER noticed that patients arrive to the hospital at a rate of 5 individuals per hour,
and the time between patient arrivals was Exponentially distributed.
Let X = the time between patient arrivals at the ER.
Figure 3.1: The probability density function of the time between patient arrivals.
4.
2.
00
0.5
10
1.5
20
In addition, recall the R commands related to an exponential distribution mentioned in the pre-reading:
<d, p, q, r>exp( x, rate),
where
рехр:
CDF function: F(x) = P(X sx)
dexp:
PDF function.
rexp:
Random draws from an Exponential distribution,
:dxeb
Gives the quantile function.
Let's find some probabilities and quantiles:
1. Find the probability that the time between patient arrivals is
a. 30 minutes or less.
b. Between 30 minutes and one hour.
c. At least one hour.
[Hint: An expression for a probability can look like one of the following:
P(a < x < b), P(a sXs b), P(a s X < b), P(a < X), P(a s X), P(X > b), P(X 2 b), etc.]
2. Find the first quartile, median, and third quartile of X. That is, find a value q, such that
F(q) = P(X <q) = 0.25, 0.5 and 0.75.
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