1. L

    generating functions

    How can I continue this problem. my aim is to write a closed form. ( the first line is the original question given, the rest is I have written )
  2. S

    Problem with generating safe primes

    So I'm using the Lucas primality test to generate large primes. The factorization of N-1 is known of course and in this case I'm just using randomized powers 2 and 3. That part works fine and it produces plenty of primes. Now what I really want is "safe primes". Since I've already verified that...
  3. J

    Joint Moment Generating Function from Conditional and Marginal Distribution

    Suppose that that random variable $N$ follows a Poisson distribution with mean $\lambda=6$. Suppose that the conditional distribution of the random variable $X$, given that $N=n$, follows that of a $Binomial(n,0.6)$. Find the Joint Moment Generating Function of $(N, X)$. Initially I just...
  4. J

    Problems finding the Moment Generating Function

    Let the random variable X equal the number of flips of a fair coin that are required to observe heads - tails on consecutive flips. Find the pmf of X and find the moment generating function of X. The PMF is straightforward since there are always two desired outcomes divided by 2^n (where n...
  5. J

    Moment generating function for a random variable described by a piecewise pdf

    Part e) is the problem in question here; I'm not exactly sure how to find the moment generating function, specifically when 1 <= y < 2. I know that M(t) = the integral from -infinity to infinity of e^(tx)*f(x)*dx, but do I simply use 2-y for f(x) on that interval? I'm not exactly sure, I think...
  6. E

    Generating a linear system for popularity calculation

    This is a half mathematical half computer science question. I am working on matlab on a mathematical problem. I want to generate a linear system for the calculation of popularity of people (a vector x) in a generic social network, given a simple matrix of friendship F. If user 1 and user 2 are...
  7. C

    Moment generating function

    If I have a sequence of independent random variables having a standard normal distribution. Suppose N has a poisson distribution with mean \lambda and is independent of this sequence. Define a new random variable W = sum of Xi from i=0 to N. Show moment generating function of W is...
  8. O

    Generating a discrete curve over n interval with a set sum value (under curve)

    Hello all, I am trying to figure out how to generate a bunch of different curves that all fall into the same category. They take place over n (96 to 144) discrete intervals or discrete iterations (these represent months) and need to always sum up to 100,000 (dollars). So I am trying to figure...
  9. C

    Moment generating function

    Some variable Z has a poisson distribution where a > 0 Pz(i) = e^{-a}\frac{a^i}{i!} Mz(t) = e^{-a(1-e^t)} <- Moment generating function of Z Y = \frac{Z -a }{\sqrt{a}} I need to calculate the natural logarithm of the moment generating function of Y.Is my working below correct? Y =...
  10. L

    Find the generating function for the following sequence

    Hello I need to find generating function for sequence : 1,1,1,1,1,1,0,0,0,0 .... G(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + 0x^6 + 0x^7 + 0x^8 + 0x^9 ..... = 1 + x + x^2 + x^3 + x^4 + x^5 and then G(x) = \frac{1 - x^6}{1 - x} Why is There 1 - x^6? Can somebody help me to...
  11. G

    question in regards of generating a set of random triangles

    Hi. I hope this is the right forum and the right section. :) Let's assume I have the following given: - a rectangle with a given length and height - a number of triangles I want to place in it - a value specifying how random the size of the triangles should be (for example from 0 to 1, where 0...
  12. J

    How many ways you can make change for an amount N using A and B monets.

    I encountered a quite interesting problem. The question is: How many ways you can make change for an amount N using monets of value A and B, knowing that GCD(A,B)=1. Any idea how to solve this? It reminds me combinatorial class and generating functions. So i know that when we are given an...
  13. H

    Generating Function for trees

    Hi, Please I need you help to solve this problem: ---------- Consider a planar tree with $n$ non-root vertices (root edge selected). 1. Give a generating function for vertices distance $d$ from the root. 2. Proof that the total number is $$\displaystyle...
  14. H

    Generating function for vertices distance from the root in a planar tree

    Hi, Please I need you help to solve this problem: ---------- Consider a planar tree with $n$ non-root vertices (root edge selected). 1. Give a generating function for vertices distance $d$ from the root. 2. Proof that the total number is $$\displaystyle...
  15. T

    Calculating moment generating function

    I know how to calculate a moment generating function if the distribution looks like X ~ U(0,1), for instance. But if I have a uniform distribution looking like X_n \tilde \ U(0, \frac{1}{n}, ..., \frac{n-1}{n}, 1), how do I calculate M_{X_n}(t)?
  16. A

    generating expressions instead of deriving solutions

    generating expressions instead of deriving solutions All possible expressions could be generated and each one tried out as a possible solution of a given problem. Once in a while we would find it to be an actual solution. This process of generating expressions as mere combinations of symbols...
  17. A

    Probability generating function

    Hello! I have an exercise of this type that I just can not solve "Are X and Y be independent random variables, X-Poisson(a), Y-Poisson(b). Find the probability generating function of the random variable Z = 2x+3y+4 " The only thing I could do is to put into practice a property of the...
  18. S

    Methods of generating even numbers

    I have uploaded this video and I would like to share with a pro maths to verify my findings, please let me know your thoughts:
  19. R

    Homework help - Generating random variable

    Hi, I have a problem on the following homework assignment: Suppose that X and Y are discrete random variables with a joint probability mass function p_XY (x, y). Procedure is the following: a. Generate X ? p_X (x). b. Accept X with probability p(y|X). c. If X is accepted, terminate and return...
  20. S

    Generating functions

    Hi forum! If anyone can help me with this it would be a tremendous help. The answer to this problem is C(6+3-1,6) - C(3+3-1,3) - C(2+3-1,2). Here is the problem: How many ways are there to split six copies of one book, seven copies of a second book, and eleven copies of a third book between...