iid=independent and identically distributed
This is the model answer to a question which is unlikely to be wrong. I don't understand the part circled in red. How is that step justified? ~ is not the same as a equal sign, so can we still do that?
In other words, my question is "If c is a constant and cW follows the t-distribution with parameter 12, i.e. cW~t(12), does this imply that W~1/c t(12)?"
If so, WHY?
I hope that someone can help me out. Thanks a lot!
Firstly, here we are assuming alpha>0, right?
Secondly, the f(u/alpha) seems to make things complicated. I still can't see why "If c is a constant and cW follows the t-distribution with parameter 12, i.e. cW~t(12), then W~1/c t(12)". Could you explain a little bit further?
Thank you!
On behalf of the mathematics (which is the cause of the trouble), I apologise that "the f(u/alpha) seems to make things complicated".
My argument needs to be changed if because of the necessary reversal in the inequality as a result of dividing by . I should have stated that, I just assumed because that was your specific circumstance. I will let you check what the end-result will be.
I have given you a formula with a clear derivation of where it has come from. Apply the formula for your particular situation. In fact, feel free to use the derivation as a guide for deriving the formula for your own specific case.
Now I am seeing another trouble...
If X is a random variable, then I know what 1/c X means, but t(12) is a distribution, what is the meaning of saying some random variable follows the distribution 1/c t(12)?