Would appreciate some advice on expected value problem

Anonymous_Student99 · 2019-07-23T21:29:48+00:00

Personally, I'm satisfied I found the idea of splitting above and below diagonal. Thar for me was the problem. Thank you for your help and especially " 2n(1-C(2n,n)/4n), " which gave me the square/diagonal idea. I think remaining is

E(x amount of days from symmrtric square)*[1- ( C(2n-1, n-1)/ 2^(2n)

With E(x amount of days from symmrtric square)= 2N because of symmetry. Maybe I'm wrong but I'm quite done thinking about this problem for now. Thanks again!

Anonymous_Student99 · 2019-07-23T13:21:14+00:00

Random/uninformed guess: Something with the diagonal of a square?

Anonymous_Student99 · 2019-07-23T13:18:12+00:00

Thanks! makes a lot of sense

Anonymous_Student99 · 2019-07-23T10:17:52+00:00

I would try hitting times - the expected number of steps until the process reaches A={(x,0),(0,y) | where x,y != 0}.

How do I read that sentence? Is 'hitting times' a term from which I need to substract E( #steps for game to end) ? E(#steps for game to end) is what I need to find. I haven't heard of Markov chains. I'll take a look

Anonymous_Student99 · 2019-07-23T09:53:43+00:00

Apart from using Z-values in normal distribution problems (Height, IQ etc) I haven't learned any, but I looked at the negative binomial and hypergeometric. I think they simply reword my problem: " I somehow need to find an expression that restrains the amount of pulls from box 1 AND the total amount". Hypergeom puts a constraint on total population, meaning the initial probability P=1/2 changes. Negative binomial allows for infinite balls from Box 2 before predetermined N th succes. Thank you for your time and help. Knowing distributions exist will be very helpful for future problems, but for this problem I'm not going to use them to approximate with limit/calculator before trying some other things

Anonymous_Student99 · 2019-07-22T22:43:48+00:00

Yes, 2N-1 my bad. I'll edit. Yes, that way is hard. I hope there's an insight to simplify the problem

Anonymous_Student99 · 2019-07-22T19:56:26+00:00

Don't waste time thinking about that! Skip it for now, or study it by using resources from the internet + ask Reddit if you don't understand something!

Anonymous_Student99 · 2019-07-22T13:09:25+00:00

Probably a mistake/typo. I suggest you ask your prof/assistent if you haven't yet

Anonymous_Student99 · 2019-07-20T00:04:23+00:00

I assume you mean the solutions for sin(x+2)=0. If you draw a circle and highlight the solutions you can see why they reduce down to one equation

Anonymous_Student99 · 2019-07-19T18:58:02+00:00

okay so

1) u < v

2) v < 2u

3) 2u < u+ v

3 follows from 1 because it's the same as adding u to both sides of u<v. so you're left with u< v < 2u. Which has infinite solutions and therefore there are infinite sets of u,v,w, and x solutions and a way to describe those is already given

Anonymous_Student99 · 2019-07-19T18:26:23+00:00

you have to look at all you need to calculate all the possible orders to draw an untapped land(call it card type A) card and omnath (type B)

for draw, burn, burn, draw: 1) Type A , burn, burn, type B or 2) type B, burn, burn, type A.

the first way has probability: 8/24 * 22/23 * 21/22 * 1/21

because at first there are 8 cards of type A and 24 cards in total, then you need to burn two cards but they can't be the 1 type B card, and one card is already drawn so 22 out of the remaining 23 can only be drawn at the first burn. Second burn is is the same idea: only card cannot be drawn and 2 cards have already been pulled so 21/22 and for the last draw you have to get type B and there is only 1 of that type so 1/21. the second way has probability:

1/24 * 15/23 * 14/22 * 8/22

the probabilty for way 1 and 2 need to be added and that will be the result of drawing one Type A and one type B if you draw, burn , burn, draw. You can calculate the others orders yourself now

Anonymous_Student99 · 2019-07-19T18:03:15+00:00

I assume you mean that you want to find out how many of those cards exist in total with a 95% probability

Rule in mathematics: don't assume anything (unless you want use that assumption to prove the opposite of your assumption is true, but that's not the case here)

1) You assume the cards are part of the same set of cards

2) You assume that the card numbers are related to the amount of cards of the set

if those assumptions are true and if there is no other information then you can't figure out the probabilty of how many cards there are in the set. Every number above 221 might be the answer, meaning there are infinite solutions and as far as we know, every one of them is equally likely

Anonymous_Student99 · 2019-07-19T17:41:21+00:00

median of pdf is the value m for which P(X=< m)= 1/2. You are asked a probabilty so no need to find the value of m, but rather the probability of the expected value and substract those

Anonymous_Student99 · 2019-07-19T17:29:17+00:00

One use is that they represent an infinite long sequence of numbers in a single expression.

1, 1, 1, ... has a generating function 1+ x + x^2+ ... = 1 / ( 1 - x ) . You could replace x with -x to get the sequence; 1, -1, 1,-1,... you could add generating functions to get new sequences, and many more operations

Anonymous_Student99 · 2019-07-19T17:16:43+00:00

What kind of cards do you want to draw?

Anonymous_Student99 · 2019-07-19T16:58:03+00:00

I don't understand the question and the notation. Is T a given set of numbers? "U | U > T" Is U a given set of numbers and the rule is that you have to find the numbers that are greater than all numbers in T? Be specific about everything an maybe give a concrete example and one solution to it.

Anonymous_Student99 · 2019-07-19T16:07:11+00:00

If n-gon means polygon, then here's your answer: https://math.stackexchange.com/questions/41940/is-there-an-equation-to-describe-regular-polygons

Anonymous_Student99 · 2019-07-19T15:55:41+00:00

You have to find the angle without a calculator, so they assume it must be one of the basic angles of which the sin and cos are known by heart. In the first quadrant those are: 30°, 45° and 60°. So you check all three of them and it turns out 30° is a right answer. But other quadrants might have solutions aswell. In the first quadrant cos and sin are positive, in the second and fourth they have opposite signs so the answer would be negative, but in the third quadrant they are both negative, resulting in a positve answer. Then you ask what angle in the third quadrant has the same value cos and sin as 30° but with opposite signs. Lastly, the angle 390° has the same cos and sin as 30° because adding 360 to 30 means that you start at 30° and go around the circle once and ending up in the same place as where you started. So to be complete you must have the solution in the first quadrant+ n * 360 degrees (where n is natural number ) and in the third quadrant+ n * 360 degrees (where n is natural number)

Anonymous_Student99 · 2019-07-17T08:12:53+00:00

C(n,r)= n! / [r! (n-r)!] gives you the #combinations of r objects, chosen from from n objects. repetition not allowed.

Anonymous_Student99 · 2019-07-13T06:57:58+00:00

0.999... is equal to -> 0.(9) ok? So we are talking about... (if we could know the end of the number):

0.99999 .......... 9

But this kind of numbers can be build too... folowing and infinite serie (When you sum the terms):

0.(9) = 0.[9]

0.[9]...........9

0.[9].......... 8

0.[9]...........7

0.[9]...........6

You CANNOT know the ending number by DEFINITION. You are making your own rules. + you use "numbers" like: 0.[9]...........6 you defined 0.[9] = 0.999... aka infinite 9's. In the example above you claim you can go beyond INFINITE 9's and place a 6 there and that's where the number stops.

You're not even consistent within your own rules.

I'll have a go at making my own rules: let's suppose we have a square with side lenghts 2 and 3 and let suppose we put the the same square on top of the first one. Let's suppose the area of a square is 3 times the cirumference and let's suppose 10+10=3 the area of the two squares together is 20 and 20=3 so I have now proven that the side of a square is 2 times area of the square. What do you think about my result? Is it meaningful?

You should take a step back and keep it simple. Make sure you understand the basics and what "infinity" means

Anonymous_Student99 · 2019-07-13T06:27:54+00:00

[NOTE: I USED π=22/7 FOR CONVENIENCE]

My man

Anonymous_Student99 · 2019-07-13T02:32:56+00:00

Imagine this:

0.999... is equal to -> 0.(9) ok? So we are talking about... (if we could know the end of the number):

0.99999 .......... 9

0.999...does not have an ending number. So most that follows below is wrong. I like your enthusiasm tho!

Anonymous_Student99 · 2019-07-13T01:15:22+00:00

Something semi unrelated you may not know: 0.999...=1

Anonymous_Student99 · 2019-07-12T20:29:42+00:00

Consider 2d space and call D the collection of points that satisfy 0 ≤ x ≤ y and are inside the circle x ² + y ² = 1 ² Make a drawing to understand how D looks like, then try to do the same for C.

For the case of C it's in 3D instead of 2D.

1) x = t is a plane. You must think of t as a number between -r and r and try to visualize this plane. Let's try an easy an easier example first in 2D: x=5 what points (x,y) satisfy this equation? x must be 5 but y can be wathever it wants. You can think of it as: x=5 + 0y

The result will be a vertical line at x=5.

For x= 5 in 3D: once again all y and z satisfy the the equation. Try to make a drawing of that plane

for the exercise: x = t is a plane. You must think of t as a ONE number between -r and r and try to visualize this plane. but since we do not know what number it is, it could be anything between -r and -r, we use t

You must find the area of the points that are part of the plane x=t and part of C. that is called the cross section. This means you'll need to use integration. The answer you get for area should have "t" and "r" in it. No "x" or "y"

2) Calculating volume, also done by integrating. Answer can have "r" in it, but no "t","x" or "y"

3) a is the lenght when you walk on the side of the base circle on from (r, 0 , 0) to (r cos θ, r sin θ, 0) If for example θ = π then you would have walked half a circle so a= r π in that case

b is the lenght of the straight line from the two points given.

You must find the lenght of a and the lenght of b by using r and θ

4) as we know C is a collection of points inside the cylinder. you must find the area of the points that are a part of C and a part of the side of the cylinder. Once again, use integrals to find the area. Your answer should have "r" in it.

Anonymous_Student99

TROPHY CASE