We can just prove it by cases: either X ≥ Y occurs or Y > X occurs, and in either case the LHS is ≥ 0, since f and g are increasing functions.
No, it was a function of a random variable. But InteGrand's solution worked.I can't make sense out of the question.
Is it meant to be (RTP):
The point I'm making is that how can a random variable exist alone without specification of it's probability?No, it was a function of a random variable. But InteGrand's solution worked.
Look at the 2014 finals. I'm sure you still have it from back when you did the course.The point I'm making is that how can a random variable exist alone without specification of it's probability?
Example, X is gamma random variable with whatever parameters. Prove that X > 0. How does this make sense? It should be prove that P(X > 0) = 1.
It's used in many hypothesis tests, for example.No, it was a function of a random variable. But InteGrand's solution worked.
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Whilst I get why chisq is the result of Z^2 (Z~N(0,1)), where in practice does it actually get used? What's so powerful about the square of the standard normal?
Look at another simple example.Look at the 2014 finals. I'm sure you still have it from back when you did the course.
I don't even care about the distribution of X in this question. I just care that X is a random variable. And I want to find something about f(X), which is what the function does to the random variable (given that f is monotonic increasing).
It gets used a lot to understand variances and forms the basis of other distributions such as the F-distribution (which has obvious applications in ANOVA, regression etc)Whilst I get why chisq is the result of Z^2 (Z~N(0,1)), where in practice does it actually get used? What's so powerful about the square of the standard normal?
It makes perfect sense to me after seeing the earlier question. And again, I couldn't care less if it's normal or gamma or exponential or a discrete r.v.Look at another simple example.
Define f: R -> R such that f(x) = x^2 and let X be a random variable with gamma distribution, say. Prove that f(X) = X^2 > 0.
It's obvious that this is true because you're just squaring positive random variables and they stay positive. But how does it make sense alone? It should be prove that P(X^2 > 0) = 1.
The point is, random variables cannot exist alone. It needs to be associated with probabilities.
By the way, this is a Pareto Distribution with scale parameter 1 (and shape parameter alpha). This distribution is related to the "80-20" law or "Pareto principle", which you may have heard of.MInd blanking.
For my reference sake, does the 2,2 entry of the inverse approximate Var(\hat{\beta})?
For my reference sake, does the 2,2 entry of the inverse approximate \hat{\beta}?
I think double check your Var, the beta terms should end up cancelling out I think.Hang on, I'm not sure if I'm doing something wrong because I run into a circular argument.
Oh. My bad. I didn't do 1/detI think double check your Var, the beta terms should end up cancelling out I think.