Yes sorry I omitted the information about the bounds
The math tags don't seem to be working so my E[X] and E[X^2] are as follows:
Mean and Variance, Moments
It is at this point where I get slightly confused. I have just rearranged the parameters in each of the 2 equations to get the answer I obtained above. I've worked through the examples for a normal distribution, but its much more straightforward than this one.
Please bear with me for this part, as its a hurdle I can't get past for these types of questions.
Using what I've derived above:
Similarly for and then re-written in terms of :
Substituting this into the expression for the estimates are as follows?:
Then subtract the square of the first from the second to get the equations:
The left hand side of the second equation above is the sample variance (that is with rather than in it) and the right hand side is the variance of the population.
So equating the raw first two moments is the same as equating the means and variances, but in this case you will find it easier to work with the population variance than with the second moment (the algebra comes out nicer)