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
0answers
28 views

Find the Probability of 2 Numbers A and B from Interval

Two numbers A and B are selected from the interval [−3, 2] with uniform distribution. (A) What is the joint probability density function for A and B? This is ...
0
votes
1answer
22 views

Probability of event given PMF

Given a pmf $$p(k) = (1 - \beta)\beta^k$$ for $k=1,2,3,\dots$, $\mathbb{P}\left(\text{outcome is even number}\right) = ?$ The event space (the power set of positive integers) is countably infinite.
0
votes
1answer
130 views

How to prove a statistic is sufficient using conditional probability argument?

I'm trying to tackle a question, but don't know how to start it: Components of a certain type are shipped in batches of size k. Suppose that whether or not any particular component is satisfactory ...
1
vote
1answer
121 views

Tricky Probability Question not sure where to start

A bag contains x (inedible) regular rabbits and one chocolate rabbit. Two players in turn draw a rabbit at random without replacement from the bag, until the chocolate rabbit is drawn. The player ...
0
votes
1answer
243 views

Buy more lottery tickets or more multipliers?

In a given lottery, let's say my odds of winning a grand prize are $p_0$, and the grand prize has value $V$. I can either buy more tickets, at a cost $C_1$, or for each ticket, I can buy a multiplier ...
0
votes
3answers
554 views

In a raffle with 100 tickets, 10 people buy 10 tickets each. There are 3 winning tickets which are drawn at random.

What is the probability that there are three different winners? My thinking is that this is a hypergeometric set up but I do not know how to set it up. If $A$, $B$, and $C$ represent the event that ...
3
votes
3answers
102 views

Correlation of uniform variables

Let $X$ and $Y$ be independent random variables, $X,Y \sim unif(0,1)$. Let $U = \min \{X,Y\}$ and $V = \max\{X,Y\}$. Find the correlation coefficient of $U$ and $V$. I think we can assume that $U = X$...
2
votes
0answers
68 views

Picking codewords that are close

Let $[n,k,d]$ be a linear code over $\Bbb F_q$ with minimum distance $d$ and number of minimum weight codewords $N_d$. How many ways can you select codewords $c_1,\dots,c_T$ (assume $T\ll q^k$) such ...
0
votes
2answers
30 views

If $P(Y^{2} \geq k) = 0.95$ is it true that $P(\sqrt{k} \leq Y \leq 1) =0.95$

Suppose $Y$ is a random variable defined on $[0,1]$, and that we know $Y^{2} \sim \mathrm{unif}[0,1]$. Suppose I determine the value of $k$ for which $P(Y^{2} \geq k) = 0.95$. Would it be correct ...
1
vote
0answers
58 views

Weak * topology on a finite-dimensional simplex

I'm trying to endow a set of probability measures $\triangle\left(X\right) $ with the weak * topology, where $X=\left\{ x_{1},\, x_{2},\,...,\, x_{N}\right\} \subseteq\mathbb{R}$ is a finite set of ...
1
vote
2answers
170 views

Probability of randomly selected balls being different colors

An urn contains 5 red and 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that they are all of the different colors if the balls are drawn without ...
0
votes
0answers
67 views

Distribution of the quotient of two random variables

Let $x$ and $y$ be two random variables with support of $\left[1\hspace{5pt}10\right]$ and $\left[50\hspace{5pt}90\right]$ respectively. The distribution of each of these variables is $p_X(x)$ and $...
1
vote
1answer
43 views

Cumulative Distribution Function with New Random Variable

I'm really new to statistics and probability so sorry if this is a really basic question. I just wasn't sure how to do it. I tried looking it up but can't find much information. If I'm given a cdf ...
2
votes
1answer
61 views

Conditional expectation of discrete random variable given noisy observation

Suppose we have discrete random variable given by \begin{align*} P(X=x_i)=\frac{1}{N}, i=1...N \end{align*} and Gaussian r.v. $Z \sim \mathcal{N}(0,1)$. Assume $Z$ and $X$ are independent. Suppose $X$...
1
vote
1answer
53 views

Probability on $C(\mathbb{R})$

Let $C(\mathbb{R})$ be the set of continuous and bounded functions $\mathbb{R}\to\mathbb{R}$. Is there a probability measure $p$ on $C(\mathbb{R})$ such $\forall g\in C(\mathbb{R}),\ \forall \...
0
votes
1answer
36 views

Sampling from a population

I have a very basic propability question: There are 200 socks in my basket. 25 are white, the rest are black. If I pick 10 socks, what's the probability of picking 3 white ones? I tried to calculate ...
1
vote
1answer
110 views

Expected number of transition events to complete multiple synchronized Markov chains

Assume the expected number of transitions (events) it takes until a Markov chain with $G+1$ states ranging from $s=0$ to $s=G$ is completed is $M$. Suppose we have $K$ independent instances of this ...
2
votes
1answer
26 views

Find the expectancy of $X$

Let $p,q \in (0,1)$. Let $Y$ be the R.V denotes the number of days of the storm in the ocean. $Y\sim \text{Bin}(n,p)$. Let $X$ be the number of ships drowned during the storm and we know that the ...
0
votes
1answer
33 views

A Bayesian problem of coin tossing

A box contains $3$ coins . Among these three , each of two coins have the probability of giving head $\dfrac 23$ and the remaining one have the probability of turning head $\dfrac 12$ . One coin is ...
0
votes
0answers
54 views

subtracting mean of iid RVs increases mutual information?

I have a problem about intuition: substracting the mean of iid RVs seems to increase the mutual information. Say $X,Y$ are real iid RVs, then $\frac{X-Y}{2}$ and $\frac{Y-X}{2}$ are not independent ...
0
votes
2answers
38 views

probabilityproblem

A and B play a game of chess. They play 20 games of which A wins 12 and B wins 4.The remaining 4 games are drawn.If 3 games are played between them, find the probability that i)B wins at least 1 game?...
0
votes
2answers
98 views

What is the expected number of trials until at least $m$ successes without repetitions?

I tried to look for a similar question but didn't find the exact thing (the closest I found was this but AFAIK it is not the same) I have $r$ coins that land heads w.p. $p$. I want at least $m$ heads....
1
vote
1answer
95 views

Markov Chain with heterogeneous transitions

I have a Markov chain as follows: $G+1$ finite states, it begins from $s=G$ and completes at $s=0$ A transition ($s\to s-1$) occurs in case if event $A$ happens. No other form of transition is ...
0
votes
3answers
80 views

Conditional probability problem of three choices [duplicate]

I have the following problem where I have difficulties grasping the intuition: Lets say we have three boxes, with two of them empty and one containing a gold price. Lets say we randomly select ...
0
votes
0answers
56 views

Why is the probability that two independently sampled values have the same value is zero?

In a book about machine learning, it reads, Generally, the probability that $x$ generated independently by a continuous probability distribution $p(x)$ have the same value is zero. Otherwise, $\...
0
votes
1answer
92 views

Expected Value Problem of a weird coin game

Consider the following game of chance. A fair coin is tossed until the first tails appears. You place an initial bet of k. If the 1st tails appears on the nth toss, you receive a total of $2^n$ (2 to ...
2
votes
0answers
36 views

Definition of Standard Deviation

We note that given a probability distribution function $P$ over a space $U$ the expected value of a function of the elements in U: $$ E(f(x)) = \int_{U} f(x)P(x) $$ We thus consider the mean as the ...
1
vote
1answer
156 views

Probability of matching sequences, and hamming distances.

Having two binary numbers of length 6, what is the probability that they match exactly? What is the probability that they have hamming distance of exactly 1? or of 2? For the first part, the ...
3
votes
3answers
3k views

Blackjack Probability

Suppose that you are playing blackjack against the dealer. In a freshly shuffled deck (standard $52$ cards), what is the probability that neither of you are dealt a blackjack. Blackjack being $2$ ...
1
vote
1answer
1k views

Proof for Standard Deviation Formula for a Binomial Distribution

I understand the concept of standard deviation as the square root of the square of the mean of each sample value - the mean of the sample values. Here is the mathematical representation (I've solved ...
2
votes
0answers
45 views

Probability sequence

Fifty marbles numbered 1 to 50 are placed in a barrel and twenty drawn one at a time without replacement. What is the probability that at least one will be drawn in sequence? i.e. 1 is drawn first, ...
-1
votes
2answers
57 views

What is the Probability of event occuring?

I am probably missing something obvious but here goes: Lets say we have ten people, and over a period of five days, five of them die. One does each day The probability of any person dying on Day 1 is ...
1
vote
1answer
38 views

How to find the pdf of difference of r.v

How do I calculate the pdf for the following case? In general, if we have 2 r.v. $x,y$ which are normal, then the pdf of the difference of 2 r.v. which are Gaussian will also be Gaussian, I think ...
0
votes
0answers
360 views

Integral of the product of two Normal distribution CDF (erf)

How do I solve the following? $$ \lim_{x \rightarrow \infty} \int_0^{x} \left[ 1 + \text{erf} \left( \frac{\epsilon - a}{b} \right) \right] \left[ 1 + \text{erf} \left( \frac{\epsilon - c}{d} \right) ...
1
vote
1answer
29 views

Find distribution of Random Variable and prove convergence in distribution.

Here is the problem that I'm solving: So a) was quite easy (if I didn't miss anything :) ) Now for b): my CDF does converge to Exp(1) when x is from 0 to n But if x more then n my function is ...
0
votes
1answer
34 views

Simplest way to solve this card problem

In a Poker match, asumming 52 cards (13 of each type). This is the state: On my hand I have cards [3] and [4] of any type. In table, there are these cards: [1] [2] [3] [?] [?], this is, two unknown ...
1
vote
1answer
992 views

distribution of the sum of two random variables convolution or not

Given $$X_1\sim f_{X_1}(x_1)$$ and $$X_2\sim f_{X_2}(x_2)$$ are independent Random Variables, does this mean that $$Z=X_1+X_2$$ has distribution $$f_Z(z)\sim f_{X_1}f_{X_2} $$ or does it mean that ...
2
votes
2answers
37 views

Convergence of the product $\prod_{i=0}^{b^\frac n2 -1} \left(\frac{b^n-i}{b^n}\right)$

Suppose we have a set of $b^n$ different numbers. Every time we randomly choose a number from this set and put it in a list of length $b^\frac n2$. So we want to fill this list with unique numbers. ...
7
votes
1answer
194 views

Occupying seats in a classroom

Here's a nice probability puzzle I have thought about for a class I'm TAing, I'm curious to see different solutions :) It goes like this: We have a classroom with $n$ seats available and $m \leq n$ ...
-1
votes
1answer
60 views

Sampling demonstration using combinatorics

Suppose that I have a finite population of A's and B's, with properties: Population size: $n$ There are $n_1$ A's and $n - n_1$ B's (so that $p = \frac{n_1}{n}$, $q = \frac{n - n_1}{n}$) I'm ...
-1
votes
1answer
33 views

Probability Poker Question

You are dealt $20$ cards. What is the probability you have all kings given that you hold at least one king? So I set it up like $$ P(4\textrm{ Kings | at least one king}) =\frac{{4 \choose 4}{48 \...
-1
votes
1answer
104 views

drawing ball from an urn with replacement

Suppose we have an urn with $N$ white balls and $M$ black balls. Suppose we draw $n$ balls and each time a ball is drawn, then we put it back. Let $X =$ number of white ball we get. Let $U = \{1,2,...,...
-1
votes
1answer
67 views

How many people could be wrong in telling a coin? [closed]

If we have two coins of radius of $R_1=8$ and $R_2=12$. Assume that 99% of people will be able to tell the size within $\pm5\%$ by touch it only, and assume it is a normal distribution. Question A: ...
-1
votes
1answer
25 views

Calculating $P(X=Y)$ for geometrically distributed random variables [closed]

I want to calculate $P(X=Y)$, where $X,Y$ are independent and geometrically distributed, which means: $P(X=k) = P(Y=k) = p(1-p)^k$, $k \in \mathbb N_0$ and $p \in (0,1)$. Can anybody tell me how to ...
0
votes
2answers
150 views

Probability of infinite intersection.

I came to the following problem: Let $A_1, A_2, ...$ be events in a probability space $(\Omega, F, \mathbb{P})$ and $\mathbb{P}[A_j]=1$ for all $j>1$. I need to show that the probability of the ...
0
votes
1answer
30 views

Expected number of draws to get n number of one object

I have been playing a game and came up with this question: There are $n$ different object, and each time you randomly choose one of them. One success is defined as one of the objects being selected ...
2
votes
1answer
317 views

Expected number of trials until first success

I am trying to calculate the expected number of attempts to obtain a character in a game. The way the game works is there is a certain probability in order to capture the character. Given that you ...
3
votes
1answer
95 views

Using Lindeberg’s Condition together with the Central Limit Theorem

I have the following problem: Problem. Let $ (X_{n})_{n \in \mathbb{N}} $ be a sequence of independent random variables such that $$ \mathbf{Pr} \! \left( X_{n} = \sqrt{n} + 1 \right) = \...
3
votes
2answers
86 views

How do you interpret probabilities?

I am a college student, and i have been doin probabilities since 4 years and I always had one question which puzzled me.... Its like this : If i were told to find the probability of getting a head ...
0
votes
2answers
547 views

Solving for n, n is an exponent.

If you have a sequence of random numbers ranging between 1 and 64, what is the length of a sequence that will give a 98% chance of having at least one ( 1, 2, or 3) in the sequence? Here is the ...