UoM Maths Thread

[kinslayer]

http://en.wikipedia.org/wiki/Gradian 

[scribble]

haha oh wow what?! when would be an appropriate time to use gradians even?

[bonappler]

if you have a transformation matrix and then get it in terms of another basis, when you multiply this transformation matrix that is with respect to a basis by a certain coordinate will you get the same transformed coordinate that you would get if you used the original matrix?

[Deleted User]

If X is a random variable and x is a value that X can take, is the mean of x, E

• , the same as the mean of X, E[X]? Seems a peculiar question but I just want to make sure.

[kinslayer]

If X is a random variable and x is a value that X can take, is the mean of x, E

• , the same as the mean of X, E[X]? Seems a peculiar question but I just want to make sure.

If x is a value that the random variable X can take, then x is a real number and is just a constant; it is not random. The expected value of a constant is the constant itself: .

Sidenote: is usually referred to as the expectation or expected value of X, rather than the mean.

[Deleted User]

Gotcha.

Also, I'm having difficulty interpreting this:
The distribution of X|Y=y is an exponential distribution with parameter y, α>0 where α is alpha.

So does that mean X|Y is distributed exp(y) or exp(α)? Is it even possible for X|Y to have distribution exp(y)?

[kinslayer]

Gotcha.

Also, I'm having difficulty interpreting this:
The distribution of X|Y=y is an exponential distribution with parameter y, α>0 where α is alpha.

So does that mean X|Y is distributed exp(y) or exp(α)? Is it even possible for X|Y to have distribution exp(y)?

That doesn't make much sense to me. If X|Y is exponentially distributed then it can have only one parameter by definition. It is possible for it to have parameter y, but in that case I don't know how α is relevant.

Is this from an assignment?

[Deleted User]

It's a question similar to one from an assignment, yes. So I can't post the full question. 

But the extract I posted is the only information given in relation to the distribution of X|Y. It clearly states that the parameter of the exponential distribution X|Y is y, but then mentions α>0 at the end and α is not mentioned anywhere else in the question. Unless the α is a typo? Though that's probably unlikely.

[kinslayer]

It's a question similar to one from an assignment, yes. So I can't post the full question. 

But the extract I posted is the only information given in relation to the distribution of X|Y. It clearly states that the parameter of the exponential distribution X|Y is y, but then mentions α>0 at the end and α is not mentioned anywhere else in the question. Unless the α is a typo? Though that's probably unlikely.

Probably a typo then. I assume it is meant to be y > 0. Maybe ask your tutor/lecturer.

[Deleted User]

Cheers. So if it was exp(y), the pdf of X|Y would be y*e^(-y^2)?

[kinslayer]

Cheers. So if it was exp(y), the pdf of X|Y would be y*e^(-y^2)?

The pdf would be , x,y > 0 and , y > 0

edit: fixed typo, thanks

[Deleted User]

Actually the pdf would be y*e^(-xy) right? And E[X|Y=y] = 1/y?

So if I I were to find E[X], how would I evaluate E[1/y]? If I knew the distribution of 1/Y, would E[1/y] = E[1/Y]? Thanks in advance.

[kinslayer]

Actually the pdf would be y*e^(-xy) right? And E[X|Y=y] = 1/y?

So if I I were to find E[X], how would I evaluate E[1/y]? If I knew the distribution of 1/Y, would E[1/y] = E[1/Y]? Thanks in advance.

Yes you are quite right regarding the pdf. Regarding E[X], sorry I think I am losing you here. 1/y just a number, so E[1/y] should be 1/y. Without a more complete description of the problem I'm not sure I can help much further. I'm not an expert on this myself so I don't want to give you the wrong answer 

[bonappler]

Has anyone done the practice MATLAB test for Lin Alg?

[TrueTears]

It's a question similar to one from an assignment, yes. So I can't post the full question. 

But the extract I posted is the only information given in relation to the distribution of X|Y. It clearly states that the parameter of the exponential distribution X|Y is y, but then mentions α>0 at the end and α is not mentioned anywhere else in the question. Unless the α is a typo? Though that's probably unlikely.

If the parameter of the exponential distribution is and the pdf is is conditional on the random variable , then this suggests to me that is most likely a parameter for the distribution of , but you mention is not used anywhere else in the question, then one can only conclude that it is irrelevant here.

Actually the pdf would be y*e^(-xy) right? And E[X|Y=y] = 1/y?

So if I I were to find E[X], how would I evaluate E[1/y]? If I knew the distribution of 1/Y, would E[1/y] = E[1/Y]? Thanks in advance.

The pdf is correct and the conditional expectation is correct. The rest of your statements don't make sense. , which is deterministic, however note that is a random variable and if you were trying to compute the expectation of this, then note that and you are done.

If you knew the distribution of , then you can easily compute the distribution of using transforms, which then you can easily compute the mean (either through MGFs, PGFs, or just by the definition itself)