The length of a stay at a hospital emergency deartment is the sum of the waiting

Question

The length of a stay at a hospital emergency deartment 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. The length of a stay at a hospital emergency deartment 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.
A) P(X>0.9)
B) P(X<0.5)
C) Mean and variance.

Explanation / Answer

The length of a 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:

B) P(X<0.5) =0.001

C) Mean and variance.

Expectation = a/(a + b) = 0.9090909

Variance = ab /[(a + b + 1) (a + b)2] = 0.006887

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