Support NeoGAF

[Pie Lord]

Is anyone here familiar with probability? I have a project one in due tomorrow as part of my final and I can't seem to find any good web sources to double check my work. If mostly deals with the counting principle and combinations. If anyone can look this over and see if I made any errors, I would appreciate it:

A bin contains 12 colored chips, of which 5 are red, 4 are white, and 3 are blue. If you select two chips (one at a time) at random with replacement, first count how many total outcome this experiment has and then find each probability:

total possible outcomes: 12*12 = 144

P(both are blue): 3/12 * 3/12 = 9/144

P(the 1st is red and the 2nd is white): 5/12 * 4/12 = 20/144

P(neither chip is red): 7/12 * 7/12 = 49/144

P(at least one is red): 144/144 - 49/144 = 95/144

A license plate consists of 3 letter of the alphabet followed by 4 digits (26 letters, 10 digits). Find the number of ways that a license plate can be created in each scenario:

with repetition allowed: 26 * 26 * 26 * 10 * 10 * 10 * 10 = 17576000

without repetition: 26 * 25 * 24 * 10 * 9 * 8 * 7 = 78624000

with vowels (A, E, I, O, U) and no zeroes (NO repetition): 5 * 4 * 3 * 9 * 8 * 7 * 6 = 181440

A poker hand consists of 5 cards dealt from a standard deck of 52 cards. Knowing that the cards are dealt without replacement and the order they are dealt does not matter, determine each of the following:

How many distinct poker are hands are possible: 52 C 5 = 2598960

Find the probability of the being dealt only hearts: 13 C 5 = 1287, 1287/2598960

Find the probability of the being dealt all four aces: 4 C 4 = 1, 48 C 1 = 48, 48 * 1 = 48, 48/2598960

I am not reducing my answers, if you are wondering.

 

[Memento_Mori15]

NVM solved it

 

[cpp_is_king]

total possible outcomes: 12*12 = 144

Everything checks out. I quoted the above one because the wording is ambiguous. To me, an "outcome" does not treat indistinguishable items as different. For example, let's say the blue chips are A, B, and C. If you draw A then B I would consider that the same "outcome" as if you draw B then C. The outcome, of course, being that you drew 2 blue chips. Now, if the chips were labelled, then I would consider that a separate outcome.

On the other hand, depending on the teacher's meaning, the answer you gave could be correct too.

 

[Pie Lord]

Everything checks out. I quoted the above one because the wording is ambiguous. To me, an "outcome" does not treat indistinguishable items as different. For example, let's say the blue chips are A, B, and C. If you draw A then B I would consider that the same "outcome" as if you draw B then C. The outcome, of course, being that you drew 2 blue chips. Now, if the chips were labelled, then I would consider that a separate outcome.

On the other hand, depending on the teacher's meaning, the answer you gave could be correct too.

Are you referring to that entire section or just that one question?

 

[cpp_is_king]

Are you referring to that entire section or just that one question?

Just that question. Everything else was unambiguously correct

 

[Pie Lord]

Just that question. Everything else was unambiguously correct

Gotcha, thanks for checking that out for me. As for your comment, I get what you're saying, but I think my teacher's meaning is different.

 

[cpp_is_king]

Prepping for finals and looking over the past midterms. This one problem, I got half off:
Evaluate the integral by converting to polar coordinates:
y=0 to y=1 and x=y to x=sqrt(2-y^2) (x+y) dx dy.
I converted it to:
pi/4 to pi/2 0 to csc(theta). Now this where I went wrong. The theta is correct but my limits for the radius is off. For some reason, the radius is confusing me now when I usually get it right away. Since y is going from 0 to 1, the radius would just be 0<r<1?

Is it a requirement of the problem to do this in polar coordinates? It's much easier to actually integrate it in cartesian coordinates.

 

[Memento_Mori15]

Is it a requirement of the problem to do this in polar coordinates? It's much easier to actually integrate it in cartesian coordinates.

NVM solved it.

 

[Exuro]

Hey everyone, I'm doing my last assignment for Differential Equations and this particular question is confusing me. It's a diffEQ modeling a forced spring mass system with damping. So I know how to find the general solution by finding the homogenous and particular solution.

How do I tell what kind of damping it has? Critical, over, under.

Then it asks if the mass is pushed up two meters to find the particular solution. This confuses me as I thought initial values didn't matter for particular solutions.

The equation is y'' + 2y' + 3y = 6sin(3t)

Edit: Im starting to think she just meant the solution with the initial condition rather than just the particular.

 

[TCRS]

guys a question on probabilities:

the probability that the wind speed will be 4m/s is 33%
the probability that the wind speed will be 5m/s is 46%

therefore the probability that the windspeed will be between 4 and 5 m/s is... ??

 

[cpp_is_king]

guys a question on probabilities:

the probability that the wind speed will be 4m/s is 33%
the probability that the wind speed will be 5m/s is 46%

therefore the probability that the windspeed will be between 4 and 5 m/s is... ??

There's not enough information to solve the problem, unless you meant that the probability that wind will be GREATER than 4 m/s is 33%, and LESS than 5 m/s is 46%, in which case the answer is (.33)(.46)

 

[TCRS]

Yeah that's what I meant. Thanks.

 

[rjc571]

There's not enough information to solve the problem, unless you meant that the probability that wind will be GREATER than 4 m/s is 33%, and LESS than 5 m/s is 46%, in which case the answer is (.33)(.46)

That doesn't make sense either, if P(X > 4) is .33 then P(X < 4) = .67, in which case P(X < 4) is greater than P(X < 5), which obviously can't happen as the CDF of a random variable must be non-decreasing. The question is probably supposed to say that both probabilities correspond to the wind speed being less than the specified amount (although it would still make sense if the second one is greater than rather than less than). Also you need to subtract the probabilities, not multiply them. (P(4 < X < 5) = P(X < 5) - P(X < 4))

 

[talisayNon]

Can someone confirm this for me? I have a take home test that I need a 100 on because i shit the bed on the second exam.

 

[Tha Robbertster]

Can someone explain me how to determine the impulse response for systems? I've got this exercise: transfer function H(s)=s^2/(s^(2)+2s+5)

The answer is supposed to be this:

At first, I thought I understood the method, but than it didn't seem to work all the time.

 

[coldvein]

well guys... i got a 90.7% on my math final which was just barely enough to sustain my A in the class! i did it! thank you for your assistance. i will be back next quarter for sure. :\

 

[Enkidu]

Can someone explain me how to determine the impulse response for systems? I've got this exercise: transfer function H(s)=s^2/(s^(2)+2s+5)

The answer is supposed to be this:



At first, I thought I understood the method, but than it didn't seem to work all the time.

Inverse Laplace transforms can be tricky, it's all about whether you see how to split the original expression up into partial fractions. Here's the solution:

You'll need to use a Laplace table such as this in case you didn't already know that:

 

[Tha Robbertster]

Inverse Laplace transforms can be tricky, it's all about whether you see how to split the original expression up into partial fractions. Here's the solution:
http://i.imgur.com/zBXgH.png[IMG]

You'll need to use a Laplace table such as this in case you didn't already know that:
[IMG]http://i.imgur.com/nDco9.png[IMG][/QUOTE]

I don't really get the steps that you're taking in the first and second line of your equation. Is that a special method or just something I'm not seeing?

We can use a table for most of the laplace transformations, but we sometimes have do it without it.

 

[Enkidu]

I don't really get the steps that you're taking in the first and second line of your equation. Is that a special method or just something I'm not seeing?

There is no special method going on here, with basic math skills you should be able to see that each step is equal to the last. The trick here lies in seeing what steps you need to take which is something you usually pick up by simply doing a lot of these transforms. If there's a specific step you don't get I can try and walk you through it though.

 

[Tha Robbertster]

There is no special method going on here, with basic math skills you should be able to see that each step is equal to the last. The trick here lies in seeing what steps you need to take which is something you usually pick up by simply doing a lot of these transforms. If there's a specific step you don't get I can try and walk you through it though.

Sorry, I most have had a brain fart before because now I can see what you're doing

Though I never would have thought of doing those steps myself. I guess you need to have a much better insight in math do see that.

 

[Enkidu]

Sorry, I most have had a brain fart before because now I can see what you're doing

Though I never would have thought of doing those steps myself. I guess you need to have a much better insight in math do see that.

You never really think to do it the first few times. Next time you do a transform though you might think to try something like this and it might be exactly what you need This is really more about learning how to rewrite the polynomials than any complex math.

 

[Nander]

This is finance, so not really math per se. But I hope that there is someone here who can help me anyway:

I'm having problems with the second question. How do you obtain the systematic covariance when you have two indices?

The formula for one index (and when both are using the same index) is Beta1*Beta2*Variance(index).

But now I have two indices, and furthermore I know that the two assets have different industry indices. There is no correlation between the market and the industries but there may be some between the two industries (if I understand the assumptions correctly). What's the formula in this case?

Is there a Finance-GAF out there?

 

[Kenka]

MATH-GAF, wtf.

You remember this picture from last page?

16 (8+8) teams were participating to the European football cup draw and these are the probabilities for each team in the column to draw another one from the line... and the final draw is the same as the rehearsal! What is the chance of that happening? Was there some match fixing shit?

 

[Sviatoslav]

Lol, Kenka. On a serious note though, the problem with that data table is that those probabilities are not independent.

 

[Kenka]

Lol, Kenka. On a serious note though, the problem with that data table is that those probabilities are not independent.

Meh, what do you want, it's an interesting question after all. But regarding your remark, that's taken in account, right?

 

[Sviatoslav]

Meh, what do you want, it's an interesting question after all. But regarding your remark, that's taken in account, right?

Yes but what I mean is you can't just take the probabilities of what actually occurred and multiply them together. It's more complicated than that. But if you did do it then it would say the odds are 1 in 1,927,453

 

[Kenka]

Astronomical in all cases. But as you said Svia, it's better to have a glimpse at the EL rehearsal draw before concluding that there was a fraud.

 

[Sviatoslav]

Astronomical in all cases. But as you said Svia, it's better to have a glimpse at the EL rehearsal draw before concluding that there was a fraud.

Especially since Europa League has 32 teams instead of 16. That would make the already high odds, significantly higher.

 

[Sviatoslav]

Don't know if it's correct but I'm reading on some Russian sites that the odds are 1 in 491,520

 

[Memento_Mori15]

Just wanted to say thanks math-gaf for helping me with the questions I had before. I got my Calc 3 grade today(finally) and I passed with a C after bombing the first midterm. Instead of dropping it, I decided to study more. If I didn't bombed the first midterm, I would have gotten a B but I'm just glad I passed it. I thought Calc 3 was supposed to be easier than Calc 2(got an A in that). Oh well, on to differential equations.

 

[AgentChris]

Could someone help with this question? Thanks
For what values of x does
2^x+x^4+3=0

 

[Therion]

Could someone help with this question? Thanks
For what values of x does
2^x+x^4+3=0

Well, you would need 2^x+x^4=-3. So at least one of 2^x or x^4 has to be negative to satisfy the equation. Is x real?

 

[AgentChris]

Well, you would need 2^x+x^4=-3. So at least one of 2^x or x^4 has to be negative to satisfy the equation. Is x real?

I believe. This is supposed to be a tricky question.

 

[Therion]

I believe. This is supposed to be a tricky question.

Then consider for what real values of x you have 2^x or x^4 negative. Try looking at a graph of those functions if it is not obvious.

 

[mohsinkhan]

Could someone help with this question? Thanks
For what values of x does
2^x+x^4+3=0

Did you plot it man it doesn't seem to have an intersect.

 

[AgentChris]

Did you plot it man it doesn't seem to have an intersect.

Yeah, it doesn't.

 

[twilitesparklemotion]

That's because neither 2^x or x^4 is negative on the real line.

Plot 2^x and x^4 separately. Do they ever dip below the x-axis? What happens when you add three positive values together?

 

[cpp_is_king]

2^x is always positive

x^4 is always positive

the sum of 2 positive numbers is always positive.

therefore, no solutions

 

[Lonely1]

I believe. This is supposed to be a tricky question.

All roots are imaginary. Are looking for a solution in the framework of Complex Variable algebra?

 

[SniperHunter]

has anyone here used a program called graph 4.1? I have a point series table showing distance of falling orange at a certain time. I created the graph using graph 4.1 but I can't insert the tangents, I am only able to insert tangents for quadratic or polynomial equations (which makes perfect sense since they are proper curves)....

can I get some help please??

 

[Exuro]

So I'm starting Calc 3 tomorrow. It's been a year since I took Calc 2 and am trying to refresh myself. I've heard 3 has a lot more in common with 1 than 2 though. All I know is we get into multivariables. What should I expect/refresh?

 

[Anticitizen One]

what the heck is the inverse function of f(x) = 5/2x+7 . Its from this college algebra review homework and im struggling here.

 

[Anticitizen One]

y = (5/2)x + 7

(2/5)y - (2/5)*7 = x

In other words:
f^-1 = (2/5)y-(2/5)*7 = (2/5)*(y-7)

thanks but that isn't one of the answers:

my options are:

a) f^-1(x)=5/2y - 7/2

b) f^-1(x)= 5/2x - 7/2

c) f^-1(x)=7/2-5/2x

d) f^-1(x)=2x+7/5

 

[Anticitizen One]

Unless you forgot to use brackets or I'm missing something (which is possible at 1 am with a headache) these are all wrong.

thats what I thought because every way I tried to do it didn't match any of the answers

 

[Vaporak]

So I'm starting Calc 3 tomorrow. It's been a year since I took Calc 2 and am trying to refresh myself. I've heard 3 has a lot more in common with 1 than 2 though. All I know is we get into multivariables. What should I expect/refresh?

If it's a standard multivariable calc course you'll probably only seriously need your differentiation and the more basic integration skills. Convergence of sequences/series and the more complicated integration algorithms probably won't be needed. The course should be about introducing some new ideas, and showing you how to apply the ideas of differentiation and integration to higher dimensional spaces.

 

[Partial Gamification]

thats what I thought because every way I tried to do it didn't match any of the answers

I always think of the inverse as the reflection over the line y=x

Not sure about the answers you have listed, typo?

edit: I don't know that I even read the problem correctly now.

 

[Partial Gamification]

It was actually supposed to be f(x)= 5/(2x+7).

and I see now you solved for that. The listed answers don't have the correct parameter, but I think this one is resolved; good show!

 

[Anticitizen One]

ok how about this one:

rationalize the denominator:

5/(square root 6 + square root 11)

Square root 6 would be 3 square root 2 right?

 

[Leezard]

ok how about this one:

rationalize the denominator:

5/(square root 6 + square root 11)

Square root 6 would be 3 square root 2 right?

The typical approach is to multiply the denominator and the nominator by the same thing. Hint: difference of two squares, conjugates.

 

[Treefingers]

ok how about this one:

rationalize the denominator:

5/(square root 6 + square root 11)

Square root 6 would be 3 square root 2 right?

sqrt(6) = sqrt(3*2), not 3*sqrt(2). And yeah the difference of two squares is your friend.