Mathematics, 02.03.2020 23:20 ash123463
In a certain city, the daily consumption of electric power, in millions of kilowatt-hours, is a random
variable X having a gamma distribution with mean
\mu=6 and variance \sigma^{2}=12.
(a) Find the values of \alpha and \beta.
(b) Find the probability that on any given day the daily
power consumption will exceed 12 million kilowatthours.
Answers: 2
= 6
= 12
![P(x 12)\\\\= \dfrac{1}{16}\displaystyle\int^{\infty}_{12}f(x)dx\\\\=\dfrac{1}{16}\bigg[-2x^2e^{-\frac{x}{2}}-2\displaystyle\int xe^{-\frac{x}{2}}dx}\bigg]^{\infty}_{12}\\\\=\dfrac{1}{8}\bigg[x^2e^{-\frac{x}{2}}+4xe^{-\frac{x}{2}}+8e^{-\frac{x}{2}}\bigg]^{\infty}_{12}\\\\=\dfrac{1}{8}\bigg[(\infty)^2e^{-\frac{\infty}{2}}+4(\infty)e^{-\frac{\infty}{2}}+8e^{-\frac{\infty}{2}} -( (12)^2e^{-\frac{12}{2}}+4(12)e^{-\frac{12}{2}}+8e^{-\frac{12}{2}})\bigg]\\\\=0.0620](/tpl/images/0531/0587/71e25.png)
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