1. F

    Generate a random number folowing a given distribution

    Hello, I have a question, Im not sure if there even exists a solution. I read that one can generate normally distributed random values from uniformly distributed ones. Is there a way of generating a random number, folowing a given distribution, out of a limited count of given uniformly...
  2. Chemist116

    How do I find the least number of spheres from a jar when taken at random?

    The problem is as follows: A porcelain jar has $x$ yellow colored spheres, $2x$ lightblue spheres and $3x$ black spheres. What is the number of spheres to be taken out of the jar at random and at least to affirm that we have $\frac{x}{2}$ spheres of each color?. (Assume that you are not...
  3. S

    Problem with arguing about probability mass of general random variable

    (I'm not sure if this is the right sub-forum, but I didn't see a better fit.) I have a problem with an exercise in a machine learning text-book. Solving it doesn't require any knowledge of machine learning, though, just of advanced probability theory. It's a very simple exercise in principle...
  4. L

    Random walk returns home

    How does one show that a random walk eventually returns to its origin?
  5. K

    Standard deviation on scaling of random variables

    I have the answer already (based on simulations), but want to know exactly which theorem/ law is at play: Suppose X1, X2, X3, X4 are 4 positive random variables such that X1+X2+X3+X4=1. Suppose I scale them with known constants C1, C2, C3, C4, respectively, then look at the function below...
  6. K

    Central Limit Theorem for weighted summation of random variables?

    Here is a quick question:- If X1, X2, X3,.... X20 are 20 random variables (independent/ idd) What would be the result of: 2*X1+5*X2+1*X3+18*X4...+0.5*X20? (linear combination of the random variables, with fixed known constants). Will the above function form a normal distribution if we...
  7. K

    Convergence of mean of inf series of random variables with different distributions

    Please see the attachment figure. I have an arithmetic mean of an infinite series of independent random variables. However, these variables can come from 5 different independent normal distributions, and each of the 5 distributions are equally probable (each having its own mean and standard...
  8. K

    Linear combination of random variables, convergence for a large number of variables

    Hi, I have positive random variables X1, X2, X3, ..., Xn such that their sum=1 (so they are random, subject to constraints that each Xi is positive their sum has to be 1.. so all are fractions). Now, I have a function f=C1.X1+C2.X2+C3.X3.....+Cn.Xn where C1, C2, ....Cn are known...
  9. M

    Independent discrete random variables probability

    Independent random variables X, Y, Z take only integer values: X - from 0 to 7, Y - from 0 to 10, Z - from 0 to 13. Find the probability P (X + Y + Z = 4) if it is known that the possible values of X, Y, and Z are equiprobable. The solution is attached below; however, I don't understand where...
  10. D

    Calculate probability of interval with a random variable?

    Hi! I have studied algebra and calculus mostly (Calculus 1), not so much probability. So my problem is that I have a random variable called r that can generate any number from 1 to 100 (1 and 100 are included, interval [1, 100]). I set up a condition that if r >= 1 and r <= 75 then generate a...
  11. S

    Function Of Discrete Random Variable

    Suppose you are playing a game that costs 8 dollars to play. You flip 10 coins and, for every head, you win 2 dollars. Whats the probability you lose money?
  12. J

    Random Sum of Random Variables

    There are 400 individuals, each of whom has a 0.2 chance of incurring a claim. If the distribution of the individual claim amount, given that a claim has occurred, is uniform on the interval [0, 200]. Find the mean and variance of the total claim. I calculated the mean of total claim...
  13. J

    Sampling Distribution of Normal Random Variables

    Let $X_1,X_2,...,X_m$ be i.i.d. from a $N(\mu_1,\sigma_1^2)$ distribution, and let $Y_1,Y_2,...,Y_n$ be i.i.d. from a $N(\mu_2,\sigma_2^2)$ distribution, and let the $X_i$'s be independent from the $Y_j$'s. Determine the sampling distribution of the following quantity...
  14. J

    Limit of Product of iid Random Variables

    Let $X_1, X_2, ... , X_n$ be i.i.d random variables with common density function: $f(x)=\frac{\alpha}{x^{\alpha+1}}I(x\geq 1)$ where $I(x\geq 1)$ is the indicator function and $\alpha >0$. Now define: $$S_n=\left[ \prod_{i=1}^{n}X_i \right ]^{n^{-1}}$$ Prove that $\lim_{n\rightarrow...
  15. C

    probability to be largest of three normal distributed random variables

    Suppose there are three random variable x1...x3, all of the normal distributed with means m1...m3 and standard deviation 1. I want to know the probability that x1>x2 & x1>x3, i.e. that x1 is the largest of x1...x3. Simple case: let us consider only 2 random variables, x1 and x2. I can then...
  16. J

    Convergence of Random Sequence

    I'm trying to understand exactly what the convergence of a sequence of random variables means. So if I have a sequence of random variables, $\lbrace X_n\rbrace$, which converges in probability to $X$, what exactly is $X_n$? I know that $X_n$ is a random variable, but how is it related to the...
  17. S

    Two random variables equal in distribution

    Hi ! Can we find two random variables that are equal in distribution but are not equal ? Thanks in advance ! :)
  18. L

    Approximated vertex cover algorithm on random graph

    I'm trying to investigate the results of running the following factor two algorithm for minimum vertex cover on random graphs. To be more specific, for a given number of vertices $n$ I'm trying to find the smallest $p$ so that running the approximation algorithm above on a...
  19. J

    Distribution of a Monotonic Function of a Discrete Random Variable

    Suppose I have a discrete random variable $Y$ with PMF $f(y)$ and support $\lbrace 1, 2, ..., N \rbrace$. Suppose I define another discrete random variable $H=Floor(Log_2(Y))$. Floor is simply the function which returns the integer part of a value, so all decimal points are truncated...