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)

0
votes
2answers
95 views

Probability Of four events

I have an issue with calculating probability of union of four events, formula listed below \begin{align*} P(A \cup B \cup C \cup D) & = P(A) + P(B) + P(C) + P(D) - P(A \cap B) - P(A \cap C)\\ &...
0
votes
1answer
15 views

Is there a name for the distribution of this CDF function?

CDF: $F(x) = (1-e^{-a \cdot x^2})^{\frac{b}{c-x}}$ where $a,b,c$ are positive constants, and $x \geq 0$. Can any body give some advice on how to analyze the mean, variance or any other properties ...
1
vote
0answers
8 views

References for the applications of probability in gambling

The intuition behind many theorems in probability comes from gamblers' games. I would like to know if there is any book or article that covers some of such connections between probability and its ...
0
votes
0answers
11 views

Game theory: how is law of large number applied here?

This is a claim rephrased and lifted from from Herbert Gintis' book "Game Theory Evolving" Pg187 Consider an evolutionary game with $n$ pure strategies $i = \{1, \ldots, n\}$, and time periods $t ...
0
votes
1answer
486 views

probability - ice cream flavours

Of the $50$ ice cream flavours at J.P. Lick’s, $10$ of the ice cream flavours have a vanilla base (as opposed to chocolate or some sort of other flavour base). Of the $50$ ice cream flavours, $15$ ...
-1
votes
1answer
28 views

does this converge? [on hold]

If I have $$X_n=\begin{cases}x_n & p_n\\ 0 & 1-p_n \end{cases}$$ and I know that $x_n$ converges to $0$ as $n$ tends to $0$, can I say that $X_n$ converges to $0$ almost sure?
1
vote
1answer
23 views

Probability of Getting a Yahtzee of Fives Given Two Fives

(The following problem is from MAML, Meet 3, Round 1, December 2012, Problem 3.) In the game of Yahtzee one has a chance to get Yahtzee (5 of the same kind, such as 5 sixes) in the throw of 5 ...
0
votes
1answer
39 views

What is the average and variation of $20$ dices?

If I roll a dice the average is $E(X) = (1+2+3+4+5+6)/6 = 7/2$ and $$E(X^2) = (1+4+9+16+25+36)/6 = 91/6$$ $$VAR(x) = E(X^2) - (E(X))^2 = 91/6 - 49/4 = 35/12$$ Now the question is: How I can find ...
2
votes
1answer
22 views

Figuring out probability of cubes with least amount of questions

Given $n$ dices with $k$ faces each numbered $1,..,k$, you're allowed to ask me what the probabilty of some event happening (a subset of all the possibilities and I give a number), what is the least ...
-2
votes
2answers
47 views

Expected number of tosses to get 3 consecutive Heads

I have a fair coin. What is the expected number of tosses to get three Heads in a row? Apparently, I could not find any completely clear approach/solution to this problem.
0
votes
2answers
24 views

Permutations in an Infinite List of Random Numbers

In an infinite list of random numbers from a to b, prove that in this list, there are all possible permutations of n numbers from the list, where n can be any number. Here are some versions of the ...
1
vote
1answer
16 views

Finding the method of moments estimator for the Uniform Distribution

Let $X_1, \ldots, X_n \sim \text{Uniform}(a,b)$ where $a$ and $b$ are unknown paramaters and $a < b$. (a) Find the method of moments estimators for $a$ and $b$. (b) Find the MLE $\hat{a}$ ...
6
votes
1answer
184 views
+200

Is there any probability model for multi-stage motion of an object such as this.

I have this following case (please refer to attached pic below) where a particle is resting on the ground and it needs a minimum amount of force (Fmin) to reach from one level to the next level. But ...
1
vote
1answer
37 views

Simple problem in probability

You have 100 lightbulbs. Every lightbulb is either functioning or not. You test 20 of them, and all of the 20 are functioning. What is the probability that 10 of the 100 lightbulbs do not function? ...
0
votes
0answers
22 views

how many samples needed to obtain an estimate with a given confidence interval

Suppose an urn contains N balls of different colors. I do not know the colors nor the distributions, and I wish to determine the fraction of red balls in the urn, (R/N), to within p% with C confidence....
3
votes
1answer
25 views

Minimal value of probability according to the difference of a Levy-process

Can we conclude for a Levy-Process, that for all $\epsilon>0$ holds $\min_{s\in [0,t]}P\left(\left|X_t-X_s\right|\leq \epsilon\right)>0$? Stochastic continuity doesn't seem to work, and the ...
1
vote
1answer
22 views

Betting ended after nth round.Find the sum of money NOT WON?

Rahul and Vijay are playing a game with 12-sided die,where both of them lay bets on outcomes of roll of die.They start betting Rs 5 each on first round of the game and the amount bet in each ...
1
vote
0answers
100 views

Switching independent experiments: Does $I_A(X_1,\dots,X_n,Y_{n+1},Y_{n+2},\dots)$ converge almost surely?

Suppose there is a sequence of independent random variables $X=(X_1,X_2,\dots)$ with $X_i$ taking values in some arbitrary measure space $E_i$. Now there is a second sequence $Y=(Y_1,Y_2,\dots)$ ...
1
vote
2answers
475 views

A conditional probability problem on coupon collection

Suppose that there are $n$ types of coupons, and that the type of each new coupon obtained is independent of past selections and is equally likely to be any of $n$ types. Suppose one continues ...
3
votes
1answer
91 views

Probability of getting loops

You are given $3$ bits of lace, if ends are tied together at random, what is the probability that you end up with $2$ loops? Generalise this for $n$ bits of lace. Ok so clearly I have 6 ends to play ...
1
vote
2answers
48 views

There are 10 boxes, 15 balls; 10 red, 5 blue. Each is randomly placed in a box in an independent manner. What's E[X=the number of empty boxes?]

There are 10 boxes, 15 balls; 10 red, 5 blue. Each is randomly placed in a box in an independent manner. The red balls are placed in boxes 1-10, blue balls are placed in 1-6. What is the expected ...
1
vote
0answers
17 views

Calculate probability of an event occurring exactly once in an arbitrarily selected year, given mean annual occurrences over a century

If an event occurs an average of 0.6 times/year over a century, what is the probability that it occurs exactly once in a randomly selected year? I was able to find p(occurs exactly once in a given ...
1
vote
0answers
26 views

Lindeberg condition's counterexample (central limit theorem)

My aim is to find an example where CLT is true but not the (equivalent to Lindeberg's) condition: Find a sequence of indipendent $(X_k)\sim\mathcal{N}\left(0,\sigma^2_k\right)$, so that they respect ...
0
votes
0answers
21 views

conditional expected value and not mutual indipendent events [on hold]

Let be $E,G,H$ pairwise independent events but not mutual (e.g. $\mathbb{P}(E\cap H)=\mathbb{P}(E)\mathbb{P}(H),\,\mathbb{P}(G\cap H)=\mathbb{P}(G)\mathbb{P}(H), ...but \,\mathbb{P}(E\cap G\cap H)\ne\...
-3
votes
0answers
23 views

if a,b are independent, can I prove that p(ab|c)=p(a|c)p(b|c) and p(a|bc)=p(a|c)? [on hold]

if a,b are independent, can I prove something below: A) p(ab|c)=p(a|c)p(b|c) B) p(a|bc)=p(a|c) thanks
0
votes
1answer
465 views

Find upper limit for this probability using Chebychev's inequality.

If $X$ is a continuous random variable which is distributed evenly in (0,10): a)How do we compute exactly $P\{|X-5| \gt 4\}$? b)Can we give an upper limit using Chebyshev's inequality and how? *Can ...
4
votes
2answers
53 views

is there a quick way to justify this elementary probability is equal to 2/3?

i just solved this problem with conditional prob. formula and after a while the answer was surprisingly 2/3 i believe there must be a tricky short way to calculate it. can somebody help me?
0
votes
1answer
35 views

Does this converge?

If I have $$X_i=\begin{cases}2\quad p=\frac{1}{3}\\ \frac{1}{2}\quad p=\frac{2}{3} \end{cases}$$ random variables with the same distribution. How can I compute the limit almost sure as $n\to\infty$ ...
1
vote
1answer
23 views

X random variable in $\mathbb{N}$ independence of events

If I have a random variable $X$ with values in $\mathbb{N}$, $$\mathbb{P}(X=n)=\frac{1}{n^s\zeta(s)}$$ where $s>1$ and $\zeta$ the Riemann zeta function, then how can I show that $$A_i=E_{p_i^2}=\...
0
votes
1answer
21 views

Prove $X$ and $Y$ are not independent

Let $X$ and $Y$ be two random variables. Their joint probability density function is $$f: (x, y) \mapsto C(y^2 - x^2)e^{-y} \mathbf{1}_A(x, y)$$ where $C \in \mathbb{R}$, $A = \{(x,y) \in \mathbb{R},...
0
votes
1answer
28 views

5 independent traffic lights, how many is car expected to pass without getting stopped

I can't wrap my mind around this one. I keep thinking it is geometric probability problem, but can't get correct solution (which is E(x) = 0.6598). Problem : There are 5 independent traffic ...
0
votes
1answer
25 views

Probability: Application Of “Expected Value”

So, I was learning expected value today and I'm trying to understand the significance of calculating this term "Expected value". In this simple example, What is the expected value when we roll a ...
1
vote
1answer
30 views

If the diameters of ball bearings are normally distributed, determine the percentage with diameters between $0.610$ and $0.618$ inches.

If the diameters of ball bearings are normally distributed with mean $0.6140$ inches and standard deviation $0.0025$ inches, determine the percentage of ball bearings with diameters Between $0.610$ ...
-4
votes
0answers
27 views

Tuition service for math CBSE [on hold]

Can anyone suggest best tuition service for CBSE 12th grade math in Kuwait?
0
votes
1answer
42 views

How to approximate the Langford numbers with probability?

A Langford pairing, also called a Langford sequence is a permutation of the multi set {$1,1,2,2, \dots, n,n$} in such a way that there are exactly $k$ elements in between every $k$. Interestingly, ...
0
votes
1answer
16 views

What is the difference between a reversible markov chain and a reversible in equilibrium markov chain?

In the text i'm using it says: "Let X = {$X_n : 0 \leq n \leq N$} be an irreducible Markov chain such that $X_n$ has the stationary distribution $\pi$ for all $n$. The chain is called reversible if ...
-1
votes
1answer
23 views

Problem involving sequence of random variables on probability space [on hold]

How do I construct (and prove that) an example of a sequence of random variables $\{X_n\}_{n\, \ge\, 1}$, on an appropriate probability space, where $X_n$ converges to $0$ in $L_r$ for all $r > 0$, ...
0
votes
1answer
60 views

Probability for a random permutation

Given a set of $N$ elements and a uniformly distributed random number generator, which always generates values between $0$ and $N-1$. Then the probability to get a random permutation (without re-draws)...
-3
votes
0answers
18 views

The odds of an event when time is a constant [on hold]

A YouTube video is 100 minutes long. In the comment section someone has placed a quote from the video. What are the odds of someone else reading this quote at the exact same time the quote is being ...
0
votes
1answer
395 views

Odds of winning a two part drawing

There is a local drawing that involves being selected out of an estimated 6000 entries, and then correctly selecting 1 of 3 numbers in order to win. The numbers have are actually cards in a deck that ...
1
vote
1answer
22 views

Showing a “signed Markov transition density” will lead to a trivial measure on path space.

Let for all $t>0$, $x\mapsto p(t,x)$ be a Schwartz function on $\mathbb R$, satisfying $\int_{\mathbb R}p(t,x)\mathrm dx=1$ and $\int_\mathbb{R}|p(t,x)|\mathrm dx\equiv C>1$ for all $t>0$ (so ...
0
votes
1answer
20 views

finding the expected value

The cones of the Lebanese cedars have (widest) circumferences that are Gamma-distributed random variables with mean of 5.40 cm and variance of 3.24 cm2 . A botanist is interested in collecting cedar ...
1
vote
1answer
23 views

Transformation of random variables that preserves the distribution

Suppose we have a random variable $X$ with distribution $F_X$. Let $X_1$ and $X_2$ be to independent copies of $X$. My question is can we find a transformation $Z=g(X_1,X_2)$ such that the ...
5
votes
5answers
19k views

Combining two probability distributions

I have a variable $X$. In a measurement $A$, $X$ follows the normal distribution $N_1$ with mean $m_1$ and standard deviation $\sigma_1$. In a similar measurement $B$, $X$ follows another normal ...
0
votes
1answer
51 views

Let's play a dice game

Roll a die with 100 faces, labeled from 1 to 100. You get to roll once and receive the amount of dollars labeled on the face. How much would you like to pay for this roll? How much would you pay ...
0
votes
0answers
20 views

Finding expected value of $E[x^{2}y]$ [on hold]

X,Y are random Variables. X = 2,4 ; Y = 1,3,5; I have to find $E[x^{2}y]$. I know that - $E[g(x)] = \sum_{r} g(x=r)P(x=r)$ But i dont know what is $E[x^{2}y]$, Somebody can help me ? Thanks.
0
votes
1answer
44 views

Conditional urn balls without replacement

An urn contains $w$ white and $b$ black balls. $n$ extractions without replacement are made. What is the conditional probability of drawing white on $8$th draw and blank on $5$th draw given that a ...
2
votes
1answer
40 views

Binary matrices and probability

Square numerical matrix in which each cell is written or the number $0$ or the number $1$ is called binary. Let $T_n -$ the set of all binary matrix $m\times m, m=2,3,...,n$. Find the probability ...
0
votes
2answers
55 views

Restrictions on Factorial Usage

I had always understood that the factorial n! was defined as $$\prod_{k=1}^nk$$ However, this leaves several questions: Why does 0! exist?* By extension, why can't you take the factorial of a ...