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  1. H

    Probability of picking fish from a tank

    Also you might want to calculate the probability that LESS than half are chosen, since P(0,1,2) are all zero. So you only need to calculate three values instead of 7.
  2. H

    A pencil game, strategy based on symmetry

    The hint you have is a pretty strong one. You really need to show us what you've come up with; then we can help some more.
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    I need help proving l^2 is a complete metric space

    Here is a thin sketch of a proof. Then you can fill in the details and ask for help on steps you don't know how to do. 1) Take a Cauchy sequence c_n in l2. Construct a new sequence X by treating each coordinate as a Cauchy sequence in R (or C). 2) Show that X is in l2. 3) Show that c_n...
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    Probability in tests in genetics

    Well let's see. Someone has the gene 93% of the time, and when they do it's reported that they have it 99.9% of the time. So out of 100k people, 930 would have the gene but the test would say no. 7% of people don't have the gene, and it's reported that they do 10.3% of the time. So out of...
  5. H

    Probability in tests in genetics

    How'd you get that? It seems close but a little too low.
  6. H

    Probability in tests in genetics

    Categorize all the people into the following: Has the gene/test says yes Has the gene/test says no No gene/test says yes No gene/test says no Figure out how many in each group. Then you should be home free to answer any questions about this test and population.
  7. H

    Probability in tests in genetics

    Well, take a stab at it yourself. You have all these tests (93.6% positive, the rest negative). How many of them are right?
  8. H

    Probability in tests in genetics

    Well, you might want to look into Bayes' Theorem (try Wikipedia). An intuitive way to do it is to create a large population, and then figure out what happens to it. So suppose there are 100,000 people. How many of them actually have the disease? Suppose we test them all. How many are...
  9. H

    Probability of x failing before y

    You need to show some work. What have you tried?
  10. H

    Game Theory a problem which is a bit similar to the Impossible Puzzle

    Well, there may be more than one solution, so you need to identify all the solutions.
  11. H

    Showing that a discontinuous function is integrable

    Hint: If you have a partition P_n, then each piece of a partition that contains a point where f is nonzero has an area of \frac{1}{n}. What you need to show is that for any \epsilon, there is an n such that no more than n\epsilon of the pieces contain a point where f is nonzero. Try to do...
  12. H

    Probability/statistics question

    No. How did you get that?
  13. H

    Probability/statistics question

    No, the question is asking for the chance that after 200 bombs were dropped, a particular block had not been hit. You are right that P(not getting hit by a single bomb) = 99/100. So what's P(not getting hit by any of 200 bombs)?
  14. H

    Linear Algebra Basis Problem

    Well xn is linearly independent and it has the same dimension as V/ker T. So it's a basis.
  15. H

    Find domain of F(x)?

    Well, suppose you want to evaluate F(3). Then you need \intop_1^9 \frac{10}{2+t^3} dt But t is supposed to be between 0 and 4, right? So this expression is undefined.
  16. H

    Sum the series p.12-15 outlines the method. The quick version: Basically you draw a square with vertices \pm (N + 1/2) \pm i(N + 1/2) . Then you show that the integral of f(z)cot(\pi z) around the square goes to zero as N-> inf. So then you get...
  17. H

    Find domain of F(x)?

    The acceptable values for t are not the same as the domain of F (ie, the acceptable values for x). I can't tell from the last comment whether you were saying that you thought that or not.
  18. H

    Limit of a composite function

    Proving that the limit of sin(t)/t is 1 as t->0 is easy, just expand sin(t) as a series.
  19. H

    Sum the series

    This series can be summed using the method of complex residues. Basically if you have a function f(z) that satisfies some weak criteria and an associated series as a function of n in the integers, you get: \sum_{k=-\infty}^{\infty} f(n) = -\pi \sum res \left[\cot (\pi z) f(z) \right]...
  20. H

    Exponetial growth?

    Well, yes, it wouldn't be correct for you to set dr/dt (the rate at which the radius is increasing per time) equal to 1900 (the size of the patch at some point in time). You want the rate at which the radius is increasing when the area is 1900. You have an expression for the rate. So evaluate...
  21. H

    Problem:residue theory

    Now you just need to do the same thing for the other poles inside your contour, except you have to expand the series around those points instead. (so the series will be in (z-pi) and (z+pi) instead of just z).
  22. H

    Problem:residue theory

    Expand 1/sin z in its Laurent series and after multiplying the various terms together, pull the residues off the 1/z term. Hint: what order pole does 1/sin z have? what's the residue of 1/sin z at 0?
  23. H

    Prove the following set is compact

    What does this mean? \Vert p - q \Vert \leq q I mean, isn't q \in K \subset \mathbb R^2 ?
  24. H

    Complex Integrals

    Yes, that's right.
  25. H

    Complex Integrals

    OK, to do this problem you need two facts: \intop_{|z|=1} z^n dz = 0, n\in\mathbb Z, n \neq -1 \intop_{|z|=1} z^{-1} dz = 2\pi i So, for example, if in the original problem, n=0, then \intop_{|z|=1} 1+3z+5z^2 dz = 0 Can you take it from here?
  26. H

    Complex Integrals

    When we talk about complex integrals, we are generally talking about something that is loosely related to the concept of line integrals in \mathbb{R}^2 . So we are going to travel along a curve (for example, the circle of radius 1 in the complex plane), and integrate the value of the...
  27. H

    Complex Integrals

    Well, what do you know about integrals of this type? It's generally required that you show us some work or something. Suppose you let n=0; that's a pretty simple thing to do. Then what is the integral? Try some different values of n. Maybe you'll see what's going on.
  28. H

    Limit evaluation. (Please confirm my work)

    Yes, this is correct. You could also use L'Hopital's rule to check, if you know about that.