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makk60
24.07.2021 •
Mathematics
I need help ASAP pls
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Ответ:
a)![E[x]= E[E[X|T]]=E[7T]=7E[T]=\frac{7}{2}](/tpl/images/0417/6263/94df0.png)
b)![Var[x] = 7E[T]+ 49 Var[T]=\frac{7}{2}+\frac{49}{12}=\frac{91}{12}](/tpl/images/0417/6263/cf148.png)
Step-by-step explanation:
A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability and is defined on a interval [a,b].
The Poisson distribution is the discrete probability distribution in order to describe the number of events occurring in a given time period. And is defined with a parameter calles usually
.
Let T the random variable that represent the number of hours between successive train arrivals at the station, and we know that the distribution for T is given by:
The expected value and the variance for an uniform random variable is given by:
ANd let X the random variable that represent the number of people who get on the next train, so the conditional distribution X|T is given by:
Since we have a Poisson distribution we can find the expected value and the variance for the random variable X|T
We can use this result in order to answer the questions like this:
Part a
Using the properties for expected value we have this:
Part b
We are interested in Var (X) and in order to find this we can use the following property from conditional probability:
And since we already found Var[X|T] and E[X|T] we have this: