59.765 probability questions.

2 Expected number of correct guess in a game

3 answers, 31 views probability probability-theory
Question is as follow. There is a bag. In the bag, there are $a$ red cubes and $b$ blue cubes. Assume that she knows exactly how many cubes for each of the colors before the draw. Mary is going to ...

Understanding statistical hierarchical models

I was given the follwoing question with solution: I however do not understand how they produced their answer. First, what general formula was used to produced the value $p(y)=\int...d\lambda$? ...

2 what is the chance of a deck of cards not having adjacent suits or numbers?

1 answers, 54 views probability combinatorics card-games
For example, if we have an Ace of spades, the next card cannot be an Ace nor spades. Edit: Assuming that we pick one particular shuffle amongst all possible ones

-1 Probability calculation from joint pdfs [on hold]

1 answers, 22 views probability integration
$f(x, y) = 6x$ for $0 \leq x \leq y \leq 1$ How do I calculate the following probability ? I haven't done double integrals in years and can't understand how this works. $P(X < 1/2, Y < 1/2)$

Marginal pdf of Jointly Distributed RVs [on hold]

$f(x, y) = 6x$ for $0 \leq x \leq y \leq 1$ How do I calculate the marginal pdfs in this equation? I haven't done double integrals in years and can't understand how this works.

5 Arrangements of Chairs in a Circle

Ten chairs are arranged in a circle. Find the number of subsets of this set of chairs that contain at least three adjacent chairs. Hints only please! This is a confusing worded-problem. We could ...

1 Properties of independence and conditional independence

Recently, I see some properties from conditional independence wiki page https://en.wikipedia.org/wiki/Conditional_independence I don't quite understand the properties of "Rules of conditional ...

2 Cauchy random variables

Considering the random variables $X_1,\ldots,X_n$, i.i.d, with Cauchy distribution, and the random variable $Y_n=\frac{X_1+\cdots+X_n}{n}$ Determinate the characteristic function of $Y_n$ and ...

3 Probability calculation for a train journey--Tail of a Binomial Distribution

Suppose the random variable $T$ which represents the time needed for one person to travel from city A to city B ( in minutes). $T$ is normally distributed with mean $60$ minutes and variance $20$ ...

3 Probability of a structure of consecutive head tosses

The exercise: A group of N friends sits around a table shaped as a regular polygon with N sides, one person on each side. Everyone tosses a fair coin once and a person is called positive if she and ...

1 equivalent definition to markov property

0 answers, 16 views probability markov-chains
A stochastic process $(X_{n})_{n \in \mathbb{N}}$ on the state space $S$ is said to be a markov chain, if it satisfies the markov propery, i.e. for all $n \in \mathbb{N}$ and $i_{0},...,i_{n+1} \in S$ ...

2 Let $X_1$ and $X_2$ be i.i.d. normal can we find the distribution of $(U_1,U_2)=(\max(X_1,X_2), \min(X_1,X_2))$

Let $X_1$ and $X_2$ be i.i.d. normal. The question is: Can we find the joint distribution of a pair \begin{align}(U_1,U_2)=(\max(X_1,X_2), \min(X_1,X_2)). \end{align} What I did Note that ...

1 Dice Tournament Probabilities

1 answers, 42 views probability matrices statistics dice
Say you were to “host” a single elimination tournament of 8 dice, each with a different number of sides: 4, 6, 8, 10, 12, 20, 24, and 30. In each round, the dice that rolls the highest wins (re-roll ...

2 Probability to choose at least one green ball and no red balls

Assume we have $n$ red balls, $n$ green balls, and unknown number of white balls. We select each ball to a set with probability $p=\frac{1}{n}$ and not choosing it with probability $1-p=1-\frac{1}{n}$...

1 Probability of an event $A$

1 answers, 25 views probability probability-theory
Let $\mathcal{Z}\subset \mathbb{R}$ be a set at most countable. Let $X,Y,Z,\xi$ random variables with the following properties: $X,Y,Z$ have value in $\mathcal{Z}$ $\xi\$ has a Bernoulli ...

32 Average Distance Between Random Points on a Line Segment

Suppose I have a line segment of length $L$. I now select two points at random along the segment. What is the expected value of the distance between the two points, and why?

3 Routine Hypergeometric Question, alternate way to solve?

1 answers, 28 views probability elementary-probability
I feel like my reasoning and solution for this question are satisfactory, but it was a multiple choice question with explicit decimals given for the options and the expression I arrived at for a ...

2 Variance of the number of copies of a random variable needed to exceed a given sum

1 answers, 45 views probability statistics
Let ${X_i}$ be independent, identically distributed, random variables each with mean $M$ and variance $\sigma^2$. Let $Y(z)$ be the number of these random variables we need to add together to exceed z,...