Solution Found!
The length of stay at a hospital emergency department is
Chapter 4, Problem 188E(choose chapter or problem)
The length of stay at a hospital emergency department is the sum of the waiting and service times. Let X denote the proportion of time spent waiting and assume a beta distribution with \(\alpha=10\) and \(\beta=1\). Determine the following:
(a) \(P(X>0.9)\) (b) \(P(X<0.5)\) (c) Mean and variance
Equation transcription:
Text transcription:
\alpha=10
\beta=1
P(X>0.9)
P(X<0.5)
Questions & Answers
QUESTION:
The length of stay at a hospital emergency department is the sum of the waiting and service times. Let X denote the proportion of time spent waiting and assume a beta distribution with \(\alpha=10\) and \(\beta=1\). Determine the following:
(a) \(P(X>0.9)\) (b) \(P(X<0.5)\) (c) Mean and variance
Equation transcription:
Text transcription:
\alpha=10
\beta=1
P(X>0.9)
P(X<0.5)
ANSWER:Solution:
Step 1 of 4:
Let us denote X is the proportion of time spent waiting assume a beta distribution with
The beta density function is
Where,
Then,
[since