The Official Math/Physics/Whatever Homework questions thread - Page 114

Thanks for the help, Wyman. Stupid question but I'm not really sure why this is right. I'm on p. 53 of Abbott's "Understanding Analysis" fwiw.

Here's the relevant part:

s_m = b1 + b2 + b3 + ... +bm (partial sums)

m <_ 2^(k+1) - 1

What is s_[2^(k+1)-1]? Abbott says it's just b1 + b2 + b3 + ... + b_[2^(k+1)-1].

k = 0: s_1 = b1
k = 1: s_3 = b1 + b2 + b3
...

What am I doing wrong here?

Also, is there any way to format these posts better? Not sure how latex (sp?) works but would be nice to make these *even* more intelligible than they already are.

Thanks again guys,
Mariogs

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04-22-2012 , 12:53 AM

#2828

BLUEberLEEZ

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Join Date: Jul 2009 Posts: 198

This is a shot in the dark. My brother is getting his masters in Econ and he has a final exam coming up on Tuesday in "Mathematical Statistics", the passing of which will determine whether or not he graduates this semester.

Apparently, this class had prerequisite courses for which he got a waiver, so it's been extremely difficult at times.

Is anyone familiar with this subject?

I don't know if it would take forever to solve the following (and show your work, if possible), but these are some ones in particular he's having trouble with...

Any help/direction would be greatly appreciated---

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04-22-2012 , 03:13 AM

#2829

Cueballmania

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Quote:

Originally Posted by Mariogs379

Also, is there any way to format these posts better? Not sure how latex (sp?) works but would be nice to make these *even* more intelligible than they already are.

There is a pretty good wikibook on latex and there is a sticky on how to include it in your posts in this forum.

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04-22-2012 , 03:14 AM

#2830

Cueballmania

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Quote:

Originally Posted by BLUEberLEEZ

Any help/direction would be greatly appreciated---

We're not doing your brother's homework for him. Also, why would he wave courses that he needs and not learn them?

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04-22-2012 , 03:34 AM

#2831

BLUEberLEEZ

centurion

Join Date: Jul 2009 Posts: 198

Quote:

Originally Posted by Cueballmania

We're not doing your brother's homework for him. Also, why would he wave courses that he needs and not learn them?

OK, I don't really browse this forum much and didn't know if someone could answer a few of these. Is anybody familiar enough with the subject material in the problems listed above to tutor him online for $20/hr? (for a few hours i guess, i don't know---you and he could work that out)

I don't know why the courses were *waived*. Thanks for your help though.

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04-22-2012 , 04:46 AM

#2832

slipstream

journeyman

Join Date: Aug 2007 Posts: 272

Quote:

Originally Posted by BLUEberLEEZ

Normally this forum is pretty helpful, but that's a big load of problems -- and to be honest, if he's struggling with problems like 6.1.1, it's likely that a forum explanation won't help him much. Can't he go to office hours or something? (Tutoring is probably a good idea also, as you suggest).

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04-22-2012 , 05:02 AM

#2833

slipstream

journeyman

Join Date: Aug 2007 Posts: 272

Quote:

Originally Posted by Mariogs379

I don't really understand what "m <_ 2^(k+1) - 1" means, or what your question is.

It seems to me that what you're saying is: s_m is the m'th partial sum of {b_i}. So
s_3 = b_1 + b_2 + b_3
s_4 = b_1 + b_2 + b_3 + b_4
s_5 = b_1 + b_2 + b_3 + b_4 + b_5
....
s_{2^{k+1}-1} = b_1 + b_2 + b_3 + ... + b_{2^{k+1}-1}.
Like when k = 3, 2^{k+1}-1 = 15 and
s_15 = b_1 + b_2 + ... + b_14 + b_15.
So it doesn't look to me like you're doing anything wrong.

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04-22-2012 , 05:04 AM

#2834

BLUEberLEEZ

centurion

Join Date: Jul 2009 Posts: 198

Quote:

Originally Posted by slipstream

ok thanks. he told me he has struggled finding anyone in his class to help him out. not sure talking to the professor is something he's done. sounds like he's exhausted the resources he has lol.

i asked him to send a swath of problems in the hopes of finding a tutor on 2p2 that could help him out for pay. he thought that was weird, so i just posted it to see if i could get answers. if anyone can and would tutor him that is pretty certain they are familiar enough with the material, just DM me i guess. test is on tuesday. thx.

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04-22-2012 , 05:11 AM

#2835

slipstream

journeyman

Join Date: Aug 2007 Posts: 272

I'll work 6.1.1 because I feel bad saying it's easy and then not doing it.

To calculate the MLE of something, you compute the likelihood function and find the value of theta that maximizes it. This means take the derivative of it and set it equal to zero, then solve for theta.

Here, we'll work with the logarithm of the likelihood function because it's just easier to handle. We get

Taking logarithms gives

Differentiating with respect to

and setting equal to zero gives

So the MLE is just the mean of the X_i's.

But again, if your brother is having deep conceptual trouble then reading a forum post is unlikely to help. Good luck to him, though.

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04-22-2012 , 08:20 AM

#2836

Wyman

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Quote:

Originally Posted by slipstream

So it doesn't look to me like you're doing anything wrong.

This

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04-22-2012 , 08:28 AM

#2837

Wyman

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Tough love: this is not the point in the semester to try to learn how to do the work. Seriously I don't understand how someone can get a masters degree in Econ without being able to do this stuff. Get a good tutor, probably an upperclassman PhD student in Econ, and expect to pay upwards of $50/hr, minimum. A good 3-4 hours will probably be a good enough "refresher" to get him a passing (but still not good) grade on the exam. But lol @ finding that for 20/hr -- this isn't teaching a 3rd grader his times tables.

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04-22-2012 , 12:02 PM

#2838

BLUEberLEEZ

centurion

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Ty Wyman and Slipstream---

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04-22-2012 , 09:13 PM

#2839

Acemanhattan

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On the topic of Econ: I have a Price Elasticity of Demand question, just wondering how to set up this equation up correctly.

PED= (% change in quantity demanded)/(%change in price) right?

Assume the price elasticity of demand for gasoline in the US is .3, and we want to see what change in price would reduce gasoline consumption by 30%.

(-.3)/x=.3
-.3=.3x
-1=x

or

(-30)/x=.3
-30=.3x
-100=x

or some other way?

I know that x needs to represent some increase in price, so I'm obviously doing something wrong when my x value ends up representing a decrease in price. It looks like price needs to increase 100%, but I'd like to show that's the case.

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04-22-2012 , 09:22 PM

#2840

Acemanhattan

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Join Date: Jan 2007 Posts: 2,978

Quote:

Originally Posted by Vael

Depends on what you're trying to use them for. If you want to assess the effect a diploma has on odds of unemployment and income, you should run a normal and a logistic regression where you control for other common determinants of these things. Otherwise, the effect you think is due to diplomas is really caused by a lot of things.

Diplomas and the like are usually taken to decrease the odds of unemployment and increase income via two channels: Signal value, a diploma signals something positive to employers, and actually making you more productive by developing your skills etc. If it's the former you're interested in, you want to include productivity related controls. If it's the latter you need panel data to take into account selection bias (more productive indivuals might be more likely to choose to get a diploma, leading you to overstimate the producitivy increase due to diplomas if you don't take it into account)

Just saw this, thanks.

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04-22-2012 , 09:40 PM

#2841

non-self-weighter

adept

Join Date: May 2008 Posts: 1,189

Quote:

Originally Posted by Acemanhattan

Often price elasticity is quoted in absolute terms, but for normal goods the price elasticity of demand is negative.

Quote:

Originally Posted by Acemanhattan

PED= (% change in quantity demanded)/(%change in price) right?

Right. Now look at the formula and think about what it means, and what kind of number you should expect. How much change in demand results from a change in price? If price increases, will demand increase or decrease?

The actual price elasticity of demand is actually -0.3.

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04-22-2012 , 10:37 PM

#2842

Acemanhattan

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Join Date: Jan 2007 Posts: 2,978

Quote:

Originally Posted by non-self-weighter

Often price elasticity is quoted in absolute terms, but for normal goods the price elasticity of demand is negative.

Right. Now look at the formula and think about what it means, and what kind of number you should expect. How much change in demand results from a change in price? If price increases, will demand increase or decrease?

The actual price elasticity of demand is actually -0.3.

Thanks. So if .3 was absolute value, then:
(-30)/x=-.3
-30=-.3x
100=x

So then if the price increases 100% (doubles) the demand for gasoline should go down by 30%.

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04-23-2012 , 10:18 AM

#2843

RaiseDaAce

adept

Join Date: Mar 2007 Posts: 865

Hi there, I have the following problem:

Suppose X and Y are two jointly distributed scalar random variables. Show that:

1) E[Y]=E[E[Y|X]]

2) E[g(Y)]=E[E[g(Y)|X]] for any function g(•)

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04-23-2012 , 10:18 AM

#2844

Wyman

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So what did you try so far?

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04-23-2012 , 10:30 AM

#2845

RaiseDaAce

adept

Join Date: Mar 2007 Posts: 865

Quote:

Originally Posted by Wyman

So what did you try so far?

calculated like this:

E[Y|X] is the conditional expectation from Y with regard to X, which is easy to calculate for either discrete or continuous variables but then if I take the expectation of the result I dont see how I get to E[Y].

the second is a tougher for me as I am not sure how to approach this

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04-23-2012 , 10:44 AM

#2846

Wyman

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Quote:

Originally Posted by RaiseDaAce

show work?

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04-23-2012 , 10:56 AM

#2847

Wyman

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I'm gonna be busy for a bit, so I'll leave you with:

Hint 1: In the first case, you have 2 sums/integrals. Switch their order.
Hint 2: Isn't Z = g(Y) just a random variable jointly distributed with X?

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04-23-2012 , 11:02 AM

#2848

RaiseDaAce

adept

Join Date: Mar 2007 Posts: 865

Quote:

Originally Posted by Wyman

show work?

E[Y|X]=sum[yij*fy(yi|x)] and here it gets tricky, I am not sure what I have to factor out of this to continue. Or do I first have to calculate E[X]somehow?