Search results

  1. L

    Cumulative Distribution Function problem

    Oh.. Ok I'm still a bit lost on how to tackle this problem..:confused:
  2. L

    Cumulative Distribution Function problem

    Homework Statement Let the independent random variables X1,X2,X3 have the same cdf F(x). Let Y be the middle value of X1,X2,X3. Determine the cdf of Y. Homework Equations F(x) = P(X<=x) = ∫-inf to x f(y)dy The Attempt at a Solution I don't understand the question, what does it...
  3. L

    Discrete Probability Mass Function

    Twenty million dollars, ten million dollars and zero dollars?? (edit)nvm I figured out ty
  4. L

    Discrete Probability Mass Function

    Homework Statement A gas supply company is trying to set up contracts with two clients, A and B. The company will make a profit of ten million dollars for each contract that is successfully agreed. The probability of agreeing a deal with client A is 1/4 and the probability of agreeing a deal...
  5. L

    Induction proof on list

    The class is known as Advanced Discrete Structures, crosslisted with Mathematics and Computer Science. Apparently we cover topics of both formal logic and abstract computer science. This is the notes we got from the professor. Maybe this would be of help...
  6. L

    Induction proof on list

    Did I finally break the experts here with an unsolvable question? Bump
  7. L

    Induction proof on list

    Homework Statement Prove by finite list induction ∀xs:: [a]. map (\x -> x) xs = xs Homework Equations map f [ ] = [ ] map f (x : xs) = (f x) : map f xs The Attempt at a Solution The list induction principle to prove a finite lists of type a is [P([ ])^ ∀x :: a. ∀xs ...
  8. L

    Solving Quartic Equation using Derivative

    Homework Statement x^4 + 3x^3 - 7x^2 - 15x + 18 = 0 Find x Homework Equations First Derivative? Second Derivative? The Attempt at a Solution Normally, I'd use Ferrari's method to tackle this problem but I am required to use derivation to find the answer... Where do I go from here? Do...
  9. L

    Finding limit

    Homework Statement Find the limit of \frac{x^3-2x^2-9}{x^2-2x-3} as x->3 Homework Equations The Attempt at a Solution You factor the bottom portion and top portion, then it looks something like this \frac{x(x^2-2x)-9}{(x-3)(x+1)} I feel like I can go further about eliminating the...
  10. L

    Finding a volume bounded by a region

    Just so that I understand, why is it that the cylindrical shell method must be applied here? I was taught that when finding a volume revolved around X or Y axis, the above equation works well except you just have to be careful when you plug in for X or Y.
  11. L

    Finding a volume bounded by a region

    Homework Statement The region bounded by y=e^-x^2, y=0, x=0 and x=1 is revolved around the y-axis. Find the volume. Homework Equations V = \int_{a}^{b} R^2 dy The Attempt at a Solution We must first express x in terms of y. So we get \ln y = -x^2 x^2 = -\ln y We substitute this to the...
  12. L

    Upper bound and lower bound

    Homework Statement 1. f(n) = n - 100 g(n) = n - 200 2. f(n) = log(2n) g(n) = log(3n) n >= 0 in all cases Find out if f(n) is an upperbound, lowerbound or both of g(n) Homework Equations The Attempt at a Solution in case of 1, f(n) has to be an upperbound of g(n) because...
  13. L

    Ascending powers math help

    Homework Statement Show that the first three non-zero terms in the series expansion of (1-1/n)^1/n in ascending powers of 1/n are 1-(1/n)^2-1/2(1-n)^3 and find the term in (1/n)^4 Homework Equations Macclaurin? Taylor? The Attempt at a Solution Can someone please point me on...
  14. L

    Continuity of the function

    [Edit] Oh, it's actually f(b-1) = 0 f(b+1) = 0 Doh! Thx
  15. L

    Continuity of the function

    Then that simply means f(b-1) = 1 f(b+1) = 1 So we have 1 = (b-1)^2 - 4(b-1) + a 1 = (b+1)^2 - 4(b+1) + a 0 = (b-1)^2 - 4(b-1) - (b+1)^2 + 4(b+1) 0 = (b-1)^2 - (b+1)^2 + 8 b = 2 Then, 1 = (2+1)^2 - 4(2+1) + a 1 = 9 - 12+ a a = 4 a + b = 6 is what I get, but...
  16. L

    Continuity of the function

    I understood why the discontinuity occurs, since |x-b|^n of n to the infinity could take you to 0 or a huge value (I think it was related to geometrical sum) depending on whether it's smaller than 1 or bigger than 1. I still do not have a clue how to get the specific values of a and b from it...
  17. L

    Continuity of the function

    Homework Statement f(x) = x^2 - 4x + a g(x) = \lim_{n\rightarrow\infty} \frac {2|x-b|^n + 1}{|x-b|^n + 1} let h(x) = f(x)g(x) Find the sum of a+b that makes h(x) continuous for all x. Homework Equations Power Series??? Derivation to test continuity??? The Attempt at a Solution...
  18. L

    Minimum value Probability Question

    Ok, it's situation like these latex seriously does a commendable job of pissing me off. How would you write the summation of index starting from j = 1 until n?
  19. L

    Minimum value Probability Question

    Homework Statement When a conventional apging system transmits a message, the probability that the message will be received by the pager it is sent to is p. To be confident that a message is received at least once, a system transmits the message n times. Assuming p = 0.8, what is the...
  20. L

    Probability Mass Function

    Ahhhh!! I should've noticed that earlier!! I was like "I have to solve a third-order equation in a probability class??" haha thanks a lot.
  21. L

    Probability Mass Function

    oh ok, then the next event is {FFS] so it's (1-p)^2 * p for the third attempt. Ok, then the total probability is p + p(1-p) + p(1-p)^2 So I set this expression equal to 0.95 and solve for p?
  22. L

    Probability Mass Function

    Probability of failing the first time is 1-p
  23. L

    Probability Mass Function

    Ok. Obviously, the probability of getting the ticket on the first call is p. Probability on the second one is 1-(1-p)^2 and the third one is 1-(1-p)^3 Then the total probability is p + (1-(1-p)^2) + (1-(1-p)^3) Am I right? And from this, do I set the whole equation to 0.95 and solve for...
  24. L

    Probability Mass Function

    Homework Statement You are a manager of ticket agency that sells concert tickets. You assume that people will call 3 times in an attempt to buy the ticket and give up. You want to make sure that you are able to serve at least 95% of the people who wants tickets. Let p be the probability that a...
  25. L

    Lagrange Triple Vector proof

    I should clarify a bit a,b,c are for cartesian orthagonal coordinates (i,j,k vectors are all normal to each other)
  26. L

    Lagrange Triple Vector proof

    Homework Statement Prove a \times (b \times c) = (a * c)b - (a*b)c For orthagonal coordinates, a,b,c Homework Equations Cross Product and Dot Product The Attempt at a Solution I thought about expanding both sides out and proving they are equal, but I just realized that the...
  27. L

    Newbie here: antiderivative for a trig function

    Welcome to PF, paretoptimal! There is a specific method to take the antiderivative of the function you've shown. Have you studied integration by parts? If no, I suggest you first read the following article to understand what it is. http://en.wikipedia.org/wiki/Integration_by_parts If...
  28. L

    Series convergence representation

    [Hits Head] Doh, of course. Thanks
  29. L

    Series convergence representation

    That's what I was thinking, except that the series is multiplied by an exponential term (with n). And sorry, there was a mistake - there shouldn't be n in the final answer.
Top