# random

1. ### 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. ### 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. ### 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. ### Random walk returns home

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