Difficult
There's not much new material in this section since the few theorems we are given are just special cases of change of variables (section 8.2). Although, this section has shown me that I still need to practice finding marginals. But other than that, the only part I had trouble with was the bivariate normal distribution example. I know the problem is mostly book-keeping, but I found it tricky manipulating the equation so that the answer comes out nice.
Reflective
Overall, this section wasn't very difficult. The special equations are nice to know in order to save time, but it's not that much harder to work it on your own. Although, it really helped to see more examples on these types of problems. It cleared up a few issues I was having earlier in section 8.2.
Thursday, December 6, 2007
Wednesday, December 5, 2007
8.3 due on 12/5
Difficult
I still don't feel fully confident about change of variables, so I think it might be hard to find if RVs U = g(X) and V = h(Y) are independent. It's not so much the concept that gives me trouble but the lack of practice. In the Uniform Distribution example, I'm not sure about the reasoning behind the solution to part (a). The solution considers a set outside C and the intersection of a set with C. I thought we just had to look at sets of (x,y) in C. Also, in the Normal Densities example, I'm completely lost on part (c). I'm not even sure what the question is asking. Perhaps if there were a picture to show what we're trying to find the probability of?
Reflective
Even though we've gone over independence before, I feel like I might still have trouble with this section. The concept is the same, just the way you compute it is different. Before, we looked at events and discrete random variables. I believe the trick is to remember that for jointly distributed, we don't look at the density f (~ p.m.f.), but rather the distribution function F.
I still don't feel fully confident about change of variables, so I think it might be hard to find if RVs U = g(X) and V = h(Y) are independent. It's not so much the concept that gives me trouble but the lack of practice. In the Uniform Distribution example, I'm not sure about the reasoning behind the solution to part (a). The solution considers a set outside C and the intersection of a set with C. I thought we just had to look at sets of (x,y) in C. Also, in the Normal Densities example, I'm completely lost on part (c). I'm not even sure what the question is asking. Perhaps if there were a picture to show what we're trying to find the probability of?
Reflective
Even though we've gone over independence before, I feel like I might still have trouble with this section. The concept is the same, just the way you compute it is different. Before, we looked at events and discrete random variables. I believe the trick is to remember that for jointly distributed, we don't look at the density f (~ p.m.f.), but rather the distribution function F.
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