I've struggled for 3 days to come up with something approaching a relevant answer but am now desperate.
Could you solve Q3, both a) and b) parts from the Exercise Sheet attached?
Happy to pay 2 credits for both answers.
Thank you very much.
3. The random variable X has an exponential distribution with mean µ. Let Y = e
(a) Use the method of transformations to find the probability density function of
Y . [ 4 marks ]
(b) Use the method of distribution functions to find the cumulative distribution
function of Y .
Here is a somewhat modified version of your presentation for the method of transformations.
I like it done in this way because I think it makes all the details transparent.
First, we write down the exponential distribution:
dP=1/μ e^(-X/μ) dX. X∈[0,∞) (1)
It may be that you are more used to start from the PDF
p(x)=dP(x)/dx=1/μ e^(-X/μ), (2)
however it is often ...
This solution explains in small details how to transform a probability distribution from one random variable to another