Hi all,
I am looking for some help since I have not dealt with a discontinuous PDF before.
The exercise is asking me to find the mean and the variance of a distribution that has the pdf:
\(\displaystyle f(x) = \frac {1}{8}\ for\ x\in [0,2)\
and\ f(x)= \frac {x}{8}\ for\ x\in [2,4)\)
My first thought was to find the mean of each part separately and add them together. I get the right answer this way. It is 31/12.
But when I tried to find the variance of each part by using the formula \(\displaystyle \ \sigma^2 = E(X^2) - \mu^2\), for each different part and then add them together I do not arrive at the right answer, which by the way is 167/144. I Instead get 375/144.
Where have I gone wrong?
I am looking for some help since I have not dealt with a discontinuous PDF before.
The exercise is asking me to find the mean and the variance of a distribution that has the pdf:
\(\displaystyle f(x) = \frac {1}{8}\ for\ x\in [0,2)\
and\ f(x)= \frac {x}{8}\ for\ x\in [2,4)\)
My first thought was to find the mean of each part separately and add them together. I get the right answer this way. It is 31/12.
But when I tried to find the variance of each part by using the formula \(\displaystyle \ \sigma^2 = E(X^2) - \mu^2\), for each different part and then add them together I do not arrive at the right answer, which by the way is 167/144. I Instead get 375/144.
Where have I gone wrong?