Mathematics, 07.03.2020 02:50, kingm6225
The waiting time for service at a hospital emergency department (in hours) follows a distribution with probability density function f(x) = 0.5exp(−0.5x) for 0 < x. Determine the following:
a. P(X < 0.5)
b. P(X > 2)
c. Value x (in hours) exceeded with probability 0.05.
Answers: 1
![\rm P(x2)= \int\limits^{\infty}_2{f(x)} \, dx \\\\ P(x2)= \int\limits^{\infty}_2{0.5\times e^{-0.5x}} \, dx \\\\ P(x2)= 0.5\int\limits^{\infty}_2{e^{-0.5x}} \, dx } \\\\ P (x2) = (0.5) \times \left[\dfrac{e^{-0.5x}}{-0.5}\right]^{\infty}_2\\\\P (x2) = (0.5) \times \left[\dfrac{e^{-0.5(\infty - 2)}}{-0.5}\right]\\\\P (x2) = 1-e^{1}\\\\P (x2) = 0.36\\](/tpl/images/0537/2309/c9ddd.png)
for x>0
![P(X2)=(0.5)[\frac{e^{-0.5x}}{-0.5}]^{\infty}_{2}](/tpl/images/0537/2309/48d16.png)
![(0.5)[\frac{e^{-0.5x}}{-0.5}]^{\infty}_{x}=0.05](/tpl/images/0537/2309/cf15f.png)
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The waiting time for service at a hospital emergency department (in hours) follows a distribution wi...
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