This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

learn more… | top users | synonyms (2)

1
vote
1answer
41 views

An Elementary Convergence Problem in Probability

Suppose that $X_1,X_2,...$ are degenerate random variables such that $f_{X_n}$ denotes the mass function of $X_n$.$$f_{X_n}(x)=P(X_n=x)= \begin{cases} 1, & x=2+\dfrac{1}{n} \\ 0, ...
2
votes
1answer
11 views

Conditional Probability of one RV having maximum among three

Let $X,Y,Z \sim \mathcal{N}(0,1)$ be independent. What is $\mathbb{P}(X>Y | Y>Z)$? I've come up with the following solution (is it correct?) but I cannot seem to understand it intuitively. ...
1
vote
0answers
37 views

When is the probability of countable union equal to the limit of probabilities of finite unions?

Lets say there are arbitrary sequence of sets $A_i$. When does the following below equation hold?, i.e., what specific properties of $A_i$ would make it invalid $$P\left(\lim_{n \to \infty} ...
0
votes
1answer
17 views

Simplifying this summation

I've been doing this question and I'm stuck! Each customer who enters Larry’s clothing store will, independently of every other customer, purchase a suit with probability p. Assume that N, the ...
1
vote
0answers
33 views

How to “reduce” a probability distribution satisfying certain conditions

I will try and explain the question I have in term of an example. I am given some probability distribution $f$, in this case of 2 variables x and p, $f(x,p)$. For example, I can pick the ...
0
votes
2answers
17 views

metrics for density-sampling similarity, beyond likelihood

I am looking for a metric that would evaluate the distance between a sample $S$ and a density function $D$ Building a sample from a known distribution can be done using a monte-carlo sampling, ...
1
vote
2answers
37 views

Probability calculation of an event.

Suppose we have a village that has the following number of total rain days every year: A1, A2, A3, ...., An for n years. With Ax an integer number of course. We want to find the probability BASED on ...
0
votes
1answer
47 views

There are 2 red, 3 pink, 4 orange, and 5 yellow jelly beans in the pocket. how many different ways can you choose at least one jelly bean?

Thanks a lot!There are 2 red, 3 pink, 4 orange, and 5 yellow jelly beans in the pocket. how many different ways can you choose at least one jelly bean?
0
votes
1answer
63 views

Formula for X “successes” with X 10 sided die.

I am trying to create a formula for the % chance of having Y number of dice hit a number 8, 9 or 10 out of X possible. For example the chance of having 7 dice out of 10 dice be one of the 3 numbers. ...
0
votes
0answers
18 views

Measurability of function with two variables. [duplicate]

Let $\phi(x,v)$ be a function from $X \times \Theta$ to $\mathbb{R}$. Here $\Theta$ is an open subset of $\mathbb{R}^k$. And $\phi$ satisfies 1.Fix $x\in X$, $v\rightarrow \phi(x,v)$ is continuous, ...
0
votes
1answer
19 views

Finding the expectation of a random variable ($E[min(X,a)]$)

I will give some context first, then i'll ask the question. Suppose you have a random variable $Y = h(X)$, such that $ h(x) = \begin{cases} 0 & x < a \\ x-a & a \leq x < b\\ b-a ...
0
votes
2answers
25 views

General approach for problems like “If a coin is tossed $n$ times, what is the probability that heads and tails appear $x$ and $y$ times”?

If a fair coin is tossed four times. What is the probability that two heads and two tails will result? I was solving the question above, since the sample space was small, I was able to list down ...
1
vote
2answers
50 views

Combinatorics using a geometric diagram

How can I do this without trial-and-error? It has something to do with a triangle and summing the next row?
0
votes
1answer
39 views

How can I solve this using permutations?

Delegates from 10 countries, including Russia, France, England and the United States are to be seated in a row. How many different seating arrangements are possible if the French and English delegates ...
2
votes
0answers
52 views

Book on Convergence Concepts in Probability without Measure Theory

I am looking for a comprehensive book on Probability which discusses Convergence of Random Variables in detail, excluding portions of Measure Theory. Allan Gut's "Probability: A Graduate Course" seems ...
0
votes
0answers
26 views

Sampling from overlapping domains

I would like to sample from overlapping domains and compute the expected number of domains sampled with every draw. As an example: Of the 20 students in Tanner's class, 8 wore a hat to school, 15 ...
-1
votes
2answers
54 views

Convolution of 2 uniform random variables

I really do not know how to do this. Let $X$ have a uniform distribution on $(0,2)$ and let $Y$ be independent of $X$ with a uniform distribution over $(0,3)$. Determine the cumulative distribution ...
0
votes
1answer
36 views

Probability of getting an average of 3 or more by rolling 4 sided die twice

What I understood is the sample mean of two rolls of all sample space(16) as given below: ...
1
vote
0answers
32 views

Probability of winning lottery

There are a total of $10,000$ tickets of which $500$ are winning tickets. Tim sells $200$ tickets. What is the probability that at least $12$ of them are winning tickets?
0
votes
0answers
18 views

What is a one-sigma Ellipse?

What is a 1-Signa ellipse? What does it represent? Also, I read the following sentence "One-Sigma lines of equal probability density of two normal distributions [(n^2 + n)/2 free parameters]" Why are ...
-1
votes
1answer
38 views

If $F(a) - F(a^{-})$ is continous then $F(a)$ is continous [closed]

Suppose $F$ is a distribution function and, $$H(a) = F(a) - F(a^{-})$$ is continous for all $a \in \mathbb{R} $, where $$F(a^{-}) = \lim_{\epsilon \to 0^+}F(a-\epsilon)$$ How to prove that $F$ is ...
0
votes
1answer
39 views

Conditional Probablity - post event

5 black balls and 11 white balls are put in a bag. 3 balls are taken out. If the fourth ball is black, what is the probability that 3 first balls are white ? Can we apply conditional probability ...
0
votes
1answer
155 views

Finding out Expected Value

After being all out for 58 and 78 in two matches in the most prestigious tournament in the world, the coach of a certain national cricket team was very upset. He decided to make the batsmen practice a ...
0
votes
0answers
12 views

The expected number of mutations in a sequence of elements, each with random delays

In a sequence, the number of the permutations, is the (minimum) number of the pair of elements needed to switch to make them sorted. For example in the following: ...
0
votes
2answers
34 views

Finding the probability that two real numbers chosen at random satisfy a set of conditions (specific problem included)

There's this easy question that's been bugging me all day long and I would be very thankful if somebody could tell me what I'm doing wrong when attempting to solve it. The problem goes: 'Two real ...
4
votes
2answers
812 views

Probability that product of any four natural numbers is divisible by 5

Given any four randomly chosen natural numbers (not mentioned if the numbers taken are distinct or not) what is the probability that their product is divisible by 5? My answers: The numbers chosen ...
0
votes
0answers
8 views

Gaussian Process: Using partitions of a choleky decomposition solution for conditional deduction.

If I define a GP over observed values, $y$, of a sensor reading over time, $t$, as (for simplicity assuming discrete time series e.g lets say readings after every 5 mins) : $y=f(t)+\epsilon$ where ...
0
votes
4answers
123 views

Prove a Continuous Distribution Function is Uniformly Continuous

Let $F$ be the distribution function for a random variable $X$ and it is given that $F$ is continuous over the entire real line. Prove that $F$ is uniformly continuous over the real line. My ...
0
votes
1answer
44 views

What is the probability that 3 out of 6 people pick the same thing in a game of rock paper scissors?

Currently my guess for a solution is [(6C3 x 3) * (3C2 x 2)] / 3^6 = 360/729 First bracket is considering 3 out of the 6 people picking the same hand to throw out (i.e rock paper or scissors) and ...
1
vote
0answers
26 views

Can you simulate from a cantor distribution?

Has someone run across a method for generating random variates from a Cantor Distribution? It seems like its abstract definition prevents this. In essence, can one "invert" the Cantor Function?
1
vote
2answers
135 views

Number of 5 letter words with at least one double letter

How many 5 letter words have at least one double letter, i.e. two consecutive letters that are the same? Answer is: $26^5 – 26*25^4 = 1,725,126 $ But how can i solve? I don't understand. The book ...
1
vote
0answers
24 views

Counting the number of integer solutions to a simple equation [duplicate]

In the following equation with unknown integers $x_i$, $1 \leq i \leq N$, the sum of all those integers are $R$. A constraint is added to each integer such that $Min_i \leq x_i \leq Max_i$. The ...
4
votes
1answer
42 views

Prove that the probability of two event sets are equal

Consider this problem: Let $A_1, A_2,...$ be an arbitrary finite sequence of events. Let $B_1, B_2,...$ be another finite sequence of events defined as follows: $B_1 = A_1, B_2 = A^c_1 >\cap ...
0
votes
3answers
28 views

Probability permutations

I'm trying to do the following probability question involving, I think, the ''amended'' multiplication rule: A Jar contains 3 red and 5 black balls. What is the probability of drawing 2 red balls ...
0
votes
0answers
65 views

Estimate probability density function of being in a certain time interval

​You arrive at a bus stop in an unfamiliar part of town. Assume that buses arrive at the stop with an unknown (to you) distribution and wait in the bus stop for a few ​minutes. The wait time ...
1
vote
1answer
64 views

Deriving the Doob Meyer decomposition of a Sub Martingale using Ito's

Given the standard brownian motion $(B_t)_{t\in\mathbf{R}_{+}}$ and defining the sub-m.g.: $$X_t =B^6_t+2t$$ I would like to derive its Doob-Meyer decomposition: [Sub-m.g.]= [increasing ...
1
vote
1answer
74 views

Expected value of prime lottery ticket

Below is a problem I think that I have solved correctly, but cannot seem to get the correct answer. Any help would be greatly appreciated. You pay $\$13.00$ for a ticket. When you buy a ticket, ...
1
vote
1answer
39 views

Conditional probability or Bayes' theorem

I'm trying to do a question in probability: ''we flip three coins'' ''What is the probability that the second coin landed tails, given that two coins (exactly) landed head?'' I have set out the ...
0
votes
0answers
17 views

Probability of helpdesk associate receiving 3 calls from same caller

Forgive my lack of knowing the lingo, but I'm curious as to how to solve this question. If there are 120 calls, 13 agents answering calls, what is the probability or the odds of one agent getting the ...
0
votes
3answers
74 views

Intro to Probability

A person randomly places 9 rooks on a 9 by 9 grid (the 8 by 8 case corresponds to a chess board). What is the probability that none of the rooks can capture any of the other rooks? I have a good ...
0
votes
1answer
33 views

Calculate probability of joint PDF

I'm given the following joint PDF and asked to calculate $P(X+Y>1)$ $f_X$$_Y$$(x,y)=2/5$ for $0<y<1$ & $0<x<5y$ and $f_X$$_Y$$(x,y)=$ $0$ else I know I have to take the ...
0
votes
2answers
29 views

Odds of failure over time.

I was having a discussion with a friend about a video game we're playing an how unlucky I've been with the odds of something occurring and I'm curious to see just how unlucky I've been. Please excuse ...
3
votes
0answers
71 views

Using Jensen's inequality to prove the Cauchy distribution has no mean

I can see that there is no mean because $\int x / \pi(1+x^{2})$ does not converge from -inf to inf. But my prof hinted at using Jensen's inequality for the proof. $$f(E(X)) \le E(f(X))$$ How can I ...
0
votes
0answers
15 views

Psudorandom number from diffrent generators.

Suppose I've N random number generators (uniform distribution) and I take 1 value from each one. Will this set of N variables be considered equivalent to N random numbers produced by a single ...
4
votes
0answers
69 views

Convergence in distribution of stochastic equation solutions

I'm studying from Kurtz's book "Markov Processes Characterization and convergence" and I have a question about the convergence of processes in $\mathbb{Z}^d$ that are solution of some equation. (see ...
1
vote
2answers
20 views

When does probability mass outside a sufficiently large ball is small?

Many times when I read books about statistics or probability theory, I encounter proofs which said: For any $\epsilon>0$ there is an $M\in(0,\infty)$ such that $\text{Pr}\{X\in ...
0
votes
1answer
58 views

Birthday paradox derivation: different approach

I usually use randomization in algorithms so I am familiar with basics of probability but nothing much advanced. I have gone through the derivation for Birthday Paradox (Cormen et al) and decided to ...
0
votes
1answer
28 views

If the side length of a square follows uniform distribution, how to find the mean and variance of its area?

A square has side of length $X$ cm, where $X\sim U[4,10]$. Find the mean and variance of the area of the square. I understand how to get the mean and variance for the length of each side, but simply ...
2
votes
1answer
72 views

Correlation of a vector generated and its one-period lag, both generated using AR(1) data

Suppose that $C_0$ is $100$ and $\{e_t\}_{t\geq 1}$ is a sequence of i.i.d. standard normal random variables. We generate $C_t=C_{t-1}+e_t$ for $t\geq 1$ and set $$ x_t=C_t^2-C^2_{t-1},\quad ...
0
votes
1answer
22 views

Basic set theory and probability

I need to prove the following but they all seem too obvious to need a proof. For the third one, for exmple, should I argue something along the line of $A\cup A^c=U$? Thanks in advance. $A=(A\cap ...