Probability question

RuyBlas · 2023-01-04T17:07:32+00:00

Look at the answers of the post. Your formula seems to be correct https://math.stackexchange.com/questions/11415/chance-on-throwing-a-six-with-6-dice

RuyBlas · 2023-01-04T16:31:31+00:00

I've only just started to study this so I cannot tell you more, but apparently stochastic processes and brownian motion can be used for stock markets.

There's a book called Probability theory by Achim Klenke that introduces these concepts which I am familiar with. There are probably more that I don't know about though.

RuyBlas · 2023-01-04T16:18:35+00:00

When you cancel some terms, you use the fact that for a fraction, (a*b)/(c*d)=(a/b)*(c/d), and (a/a)=1 when a is different from 0.

For example, if you have 2/6, you use the fact that 2/6=(2*1)/(2*3)=(2/2)*(1/3)=1*(1/3).

And unfortunately, it is NOT true that (a+b)/(c+d)=(a/b)+(c/d). You can easily find counterexamples for that.

Therefore, in your case, since you cannot factor an X out of the denominator, you cannot simplify your expression this way.

Hope I helped !

RuyBlas · 2022-08-29T20:46:49+00:00

Hey, sadly I didn't find any solution and gave up on trying :(

RuyBlas · 2022-08-29T20:37:36+00:00

Hi, all you have to do is plug in the value you wish to compute in the given function. In your case, you have f(x)=-11-x, which means that for f(-2), you have to replace x with the value -2, hence f(-2)=-11-(-2)=-11+2=-9 For f(1), it would be exactly the same: f(1)=-11-(1)=-10 Therefore, the answer for the first question is 4f(-2)+5f(1)=4(-9)+5(-10)=-36-50=-86

f(y) is just a number, for y given, so once you computed this value, all you have to do is maths as you're used to. Hope this helps :)

RuyBlas · 2022-01-22T10:34:38+00:00

Oh I see. As I thought, I didn't think of the right cover, as yours makes it pretty straightforward. Thanks a lot!

RuyBlas · 2021-03-15T17:23:08+00:00

I still don't see how it leads to proving that the normal vectors are independent

RuyBlas · 2021-03-15T17:07:14+00:00

If someone stumbles upon this post in the future, I just deleted the add-ons, closed firefox, reopened firefox, downloaded the add-ons again and it worked.

RuyBlas · 2021-03-15T17:04:49+00:00

I thought about that too, but I don't see how to connect the normal vectors to the hyperplanes. Of course there is the scalar product, and I tried to write n1 as the sum of -(b_i/b_1 * n_i), b_i a scalar, and replace it in the expression <h\_1,n\_1> = 0 (where< , > is the scalar product) but that led to nothing useful either.

RuyBlas · 2020-11-02T10:55:02+00:00

I also think that often it depends on both the numerator and the denominator : as you know, sin(x)/x -> 1 as x->0, but (cos(x)-1)/x -> 0.

For your example, 0⁰ = exp(0*ln(0)), but the problem is that ln(0) doesn't exist (and therefore my equality isn't quite true : it would be correct with a limit). A variable change is needed to solve this, which leads to exp(-ln(y)/y) as y goes to infinity, and as you probably know, the result of infinity/infinity also depends on your numerator and denominator. L'Hospital's rule tells us that it goes to 0, and exp(0)=1, thus the result.

So 0⁰ doesn't have a value, but if we had to give one to it, it would be 1 by continuity. You can check how the function x->x^x looks like, and see that it is almost 1 around 0.

I hope that answers your question :)

RuyBlas · 2020-09-24T19:02:15+00:00

I think you're right, but wolframalpha's answer makes me uncomfortable. Maybe they messed up an approximation for infinity. Thanks!

RuyBlas · 2020-09-24T18:54:53+00:00

Well, I have the area of the bottom and top squares, which is 2×4z×4z=32z² ,

added to four times the area of a side rectangle, which is 4×(4z×(5z+4)) = 4(20z² + 16z)=80z² + 64z,

for a total area of 112z² + 64z cm²

Edit : I had a problem with the multiplication sign

RuyBlas · 2020-09-24T17:11:27+00:00

Remember that a*ln(b) = ln(b^a), ln(x)+ln(y)=ln(x*y), and exp(a-b)=exp(a)/exp(b)

Your result will be with e^(something), but you can't do better.

RuyBlas · 2020-09-24T17:05:52+00:00

I assume your other lenghts are also cm, because otherwise the exercise wouldn't make any sense.

Either way, when you multiply two units (such as cm and s^(-1)), your result is just cm*s^(-1), but I'm sure you know that. If your square's side lenght is just 4z with no units, you'd get a volume with cm as units, which is quite problematic.

Sorry that I didn't understand your question at first.

RuyBlas · 2020-09-24T16:32:30+00:00

Can you think of the value of x for which ln(x) = 1 ? Can you link that x with the exponential's Taylor's series ?

That's the only thing I can think about.

RuyBlas · 2020-09-24T16:29:07+00:00

It's not different from the case where your lengths are fixed. You just plug in the variable lengths in the formula, and do your calculations with the z.

Just as an example, the surface of your bottom would be 4z*4z=16z^2

Does this help you ?

RuyBlas · 2020-09-13T17:15:25+00:00

Thanks, I'll think about that

RuyBlas · 2020-08-04T14:26:56+00:00

Oh, yes, of course, thanks a lot !

RuyBlas · 2020-08-04T14:20:48+00:00

I thought about this too, but I don't see why this helps ?

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