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 ...

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4
votes
2answers
158 views

Drunken sailor's Random Walking

A drunken walker is on $x=0$, and if $x<0$, he falls and he dies.(Once he gets position $x<0$, he dies permanently.) There is $0<p<1$ chance to move right ($x \rightarrow x+1$), and $1-p$ ...
1
vote
1answer
46 views

Probability of heads given we observe HTH?

I am observing a sequence of heads and tails and trying to deduce the bias of my coin. Let's say I observe HTH. Can I estimate the bias of my coin $p$ ? ...
1
vote
1answer
8 views

Multivariate hypergeometric distribution

The question asks: 20 individuals consisting of 10 married couples are to be seated at 5 different tables, with 4 people at each table. If 2 men and 2 women are randomly chosen to be seated at each ...
0
votes
2answers
30 views

Calculating the probability of getting a specific set of dice from a single roll

If I want to create a function $p_{roll}(x_1, x_2, x_3, x_4, x_5)$ that calculates the probability of getting the given dice (order is not important) in a single roll with 5 dice then how would that ...
0
votes
0answers
27 views

Proving convergence of events [on hold]

Let $A_1,A_2,\dots$ be events. Prove that $A_n\rightarrow A$ if and only if $I_{A_n}\rightarrow I_A$ as functions on $\Omega$, that is, $I_{A_n}(w)\rightarrow I_A(w)$ for every $w\in\Omega$. $I_B$ ...
-1
votes
1answer
31 views

Prove the inclusion-exclusion principle by probability [on hold]

Let $A_1,\ldots,A_n$ be events, and for $J\subseteq \{1,\ldots,n\}$, let $B_J = \cap_{j\in J}A_j$ . For $k\ge 1$, let $S_k=\sum_{|J|=k}P(B_J)$, where the sum is over all subsets $J$ of $\{1,...,n\}$ ...
-1
votes
1answer
37 views

Prove that the set function is a probability [on hold]

Suppose $P_1$ and $P_2$ are probability measure on measurable space $(\Omega,{\mathcal F})$ and also $\alpha$ is a real number such that $0 \le α \le 1$. Prove that the set function $P(A) = \alpha ...
-1
votes
0answers
11 views

what are the joint distribution functions and copula? [on hold]

Let $U$ and $V$ be two independent uniform (0,1) random variables and let \begin{eqnarray*} R &=&\sqrt{\frac{U^{2}+V^{2}}{2}},\\ A &=&\frac{U+V}{2}, \\ G &=&\sqrt{UV}, \\ H ...
1
vote
0answers
39 views

Fast Convergence of marginal distribtution

Let $(q_n)$ be sequence of probability density functions of the couple $(x,y)\in \mathbb R^2$, $p_n$ is the marginal density of $q_n$, i.e. $p_n(x):=\int q_n(x,y)dy$. Another sequence of functions ...
3
votes
1answer
28 views

countably additive function P

This problem comes from exercise 1.3.5(b) of 'A First Look at Rigorous Probability Theory'. It asks to give an example of a countably additive function $P$, defined on all subsets of $[0,1]$, which ...
-3
votes
0answers
42 views

Party-dance-boys-girls [on hold]

At a party,there are $n$ boys and $n$ girls.Each boy danced with exactly $k$ girls and each two boys danced with exactly $d<k$ common girls.Show that each girl danced with exactly $k$ boys and each ...
1
vote
1answer
66 views

Probability Density function help… $(X,Y) \sim f(x,y)=\frac{1}{x}$ where $I = (0 < y < x < 1 )$ …

a) show that $f(x,y)$ is a probability density function. b) $f_Y (y\mid X=x_0) =$ ? (for what $y$ is this the correct "formula"?) c) $f_Y (y) = $ ? My ideas: a) Clearly in our $I$ this is positive ...
1
vote
2answers
65 views

Probability Help! X and Y are geometric RV's with parameter p. What are …

a) $P\{X + Y = n\} (n = 1,2,...)$? b) $P\{X = k | X + Y = n\} (1 ≤ k < n)$? My work thus far... a) $\begin{align}P(X + Y = 1) & = P((X = 0 \cap Y = 1) \cup (X = 1 \cap Y = 0)) \\ & = ...
0
votes
2answers
146 views

We toss three coins (each with pr(heads)= p). Let X be the number of heads that occur on the first two tosses and Y be the number of heads..

that occur on tosses 2 and 3. range of X = range of Y = {0,1,2} Does this work seem at all correct? I am stumped with this problem... I'm not sure how to approach it. Any help is greatly ...
1
vote
1answer
78 views

Probability Help! (X,Y) ~ f(x,y) = 8xy $I_D(x,y)$

a) $f_X (x) =$ ? b) $P( X + Y < \frac{1}{2}) =$ ? c) $f_Y(y \,| \, X = \frac{3}{4}) =$ ? d) $P( Y < \frac{1}{2} \, | \, X = \frac{3}{4}) = $ ? Any help is greatly appreciated! Thanks!! Here ...
0
votes
1answer
16 views

Is there a way to use the Generalized Mean to find the “best” possible mean to use for a specific data set?

I've recently learned about the Generalized Mean as an abstraction of the many different means, includeing the Geometric, Arithmetic, and Harmonic means, as well as others. It is my understanding ...
1
vote
1answer
114 views

Conditions for convergence of moments

Let ${X_n}$ be a sequence of r.v. such that $X_n\xrightarrow [d]{}X$, with $E(X)$ finite, and with $E(|X_n|^{1+\delta})\leq K<\infty$ for all $n$. We know that: a) For $\delta>0$, we have ...
0
votes
1answer
34 views

Show that $Pr[X \gg Y]\approx 1$

Can one show (and how) that $$Pr[X \gg Y]\approx 1$$ for $$X:=\sum_{i=1}^k Bin\left(n\left(\frac{1}{2}\right)^i,i\right)$$ and $$Y:=\sum_{i=k+1}^{\infty} ...
0
votes
0answers
36 views

Prove $Pr[X + Y \geq x] \sim Pr[X \geq x]$

We have two independent random variables $X$ and $Y$, where $X=\sum_{i} X_i$ and $Y=\sum_j Y_j$, where $X_i$,$Y_j$ are (non-identically) Bernoulli distributed and independent. Under the assumption ...
0
votes
3answers
32 views

Problem on Probability

What is the proportion of numbers between $100$ and $999$ that are not divisible by $7$? please tell us the shortest method to find that kind of problems.
0
votes
0answers
49 views

Share oranges evenly

There is a boy in a street sharing his oranges with people coming across to him on a street. He has 100 oranges in his basket. The number of people walking toward the boy are unknown and varies in ...
0
votes
1answer
44 views

Quite confused about continuous probability distribution

I'm self studying probabilities and statistics, now facing this problem. Use the random variable to represent the exact number of inches yesterday rained. Then the answer showed me a figure ...
1
vote
2answers
34 views

Does $E[X]\gg E[Y]$ for independent RV imply that $Pr[X+Y \geq x] \sim Pr[ X \geq x]$?

We have two independent random variables $X$ and $Y$, where we know that $E[X]\gg E[Y]$, thus $\frac{E[Y]}{E[X]}\rightarrow 0$. I am now interested in $Pr[X+Y \geq x]$ and would like to show that ...
1
vote
2answers
86 views

What is the probability of going bankrupt in roulette?

Imagine that the bank has the money $M_1$ and the player has the money $M_2$. The rules are the following: You win with a chance of $\frac{17}{36}$ and lose with $\frac{19}{36}$ each round. Now you ...
-1
votes
4answers
52 views

A simple question of probability. [on hold]

Let p is the probability of success and q is the probability of failure in a trial.Let n is the number of independent trials,then what is the probability of success? $1.np$ $2.pq$ $3.n(1-p)$ ...
0
votes
1answer
20 views

Finding the boundaries of integration when calculating P(X + Y > a) or P(X + Y < b) (Jointly Distributed Continuous Random Variables)

I have a problem on setting the boundaries of integration when I'm trying to find probabilities like $P(X + Y > a)$ or $P(X + Y < b)$. For example, when I have $f(x,y) = \frac {x} {5}\ +\frac ...
0
votes
1answer
29 views

Linear regression as $\dim(\beta) \rightarrow \infty$

Consider the linear regression, $$ Y_i = X_i\beta + U_i \qquad E[X_i'U_i]=0 $$ where $X_i=(1,W_{i},W_{i}^2,..\ldots,W_i^K)$ and $\beta \in \mathbb{R}^{K+1}$. The joint distribution of $(X_i,Y_i)$ is ...
1
vote
1answer
38 views

Poisson approximation of $X$ by $Poisson(E[X])$

I've tried to find something, but couldn't find anything about the following question. Is it possible to approximate any random variable $X$ with $E[X]=o(1)$ by a Poisson random variable ...
2
votes
2answers
55 views

Probability of Getting a “Perfect Score” in the Card Matching Game Concentration

A person is playing the card matching game concentration. There are 40 cards, 20 pairs total. All the cards are shuffled and placed at random face down. A turn consists of two moves and a move is ...
0
votes
2answers
34 views

A Question Of Percentages

If I have 4 chances and each chance has a 10% success rate, what is the overall percent chance that 1 chance will succeed? For example: A guy plays a roleplaying game. He has 4 peices of equipment ...
2
votes
2answers
33 views

Dice Rolling 4d10 with a twist

Suppose I roll two 10-sided dice, 1 die has numbers o, 10, 20, 30 etc to 90. The second die has numbers 0, 1 ,2 etc to 9. These dice are used to create a number from 1 to 100 - example: the first ...
-3
votes
0answers
38 views

probability and statistic [on hold]

Jackie attends college on Monday, Tuesday, Thursday and Friday each week. The probability of her being late on a particular day is shown in the table below and is independent of whether she was ...
3
votes
2answers
41 views

Probability question that involves atleast

In a class 18 of the 28 students in a class bought sushi for their lunch. Suppose 12 students from that class are randomly selected. Calculate the probability that at least 11 of the 12 ...
0
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0answers
22 views
1
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0answers
30 views

On an existence of a real-valued measurable function on a non-atomic probability measure space [duplicate]

Suppose that $(X,E,μ)$ is a non-atomic probability measure space. Let $\xi :X \to \mathbb{R}$ be a random variable. A Borel measure $\mu_{\xi}$ in $\mathbb{R}$ defined by ...
1
vote
0answers
30 views

Probability density of a function of a random variable

Let $X$ be a random variable having the normal density $n(0,\sigma^2)$. Find the density of the random variable $Y = X^2$. Question: I couldn't figure out why the answers using the following two ...
0
votes
5answers
63 views

Bicycles: probability question?

I know this is quite easy but I would appreciate the help. In a survey, children were asked if they owned a bicycle. The results collected were: $46$ more pupils said ‘No’ than said ‘Yes’. ...
0
votes
2answers
91 views

probability problem explanation

To enter a cereal competition, competitors have to choose the eight most important features of a new car, from a possible $12$ features, the list the eight in order of preference. Each cereal packet ...
1
vote
0answers
37 views

Joint probability of 3 random variables when their pairwise difference is given

Consider 3 discrete random variables $X_1,X_2,X_3$ defined over $\{0..T\}$, which are identically and uniformly distributed.They are correlated in the sense that their pairwise difference has a unique ...
29
votes
5answers
4k views

Free throw interview question

I recently had an interview question that posed the following... Suppose you are shooting free throws and each shot has a 60% chance of going in (there is no "learning" effect and "depreciation" ...
2
votes
2answers
40 views

Probability that exactly 2 of 3 objects are in 1 of 3 baskets with sizes 5, 8, 2

I want to calculate the probability that some mutation occurs on a certain DNA section by a given number mutations. I rephrased it into this problem: Three (identical) persons enter a train (section ...
1
vote
2answers
70 views

Partial sum of binomial

I 'm trying to figure out a closed form solution for the following summation: $\sum_{j=0}^{\omega} j{n \choose j}p^{j}(1-p)^{n-j}$ where $\omega < n$ Is there any closed form solution?
-2
votes
0answers
27 views

Probability problem (reliability) [closed]

Assume that there are 30 cells per string. The designer is using metallic interconnects welded to the solar cells and reverse-voltage-blocking diodes connected to the ends of the cell strings by ...
2
votes
0answers
45 views

hat matching problem (Ross, p.41)

I'm studying Ross's probability book, and kind of got stuck on the matching problem. Suppose that each of N men at a party throws his hat into the center of the room. The hats are first mixed up, and ...
0
votes
3answers
36 views

Optimal stopping in coin tossing with finite horizon

There's a classic coin toss problem that asks about optimal stopping. The setup is you keep flipping a coin until you decide to stop, and when you stop you get paid $H/n%$ where $H$ is the number of ...
1
vote
2answers
38 views

Conditioning of geometric probability mass function

Problem: A group of integrated circuits is being tested. All tests are independent. The tests continue until a failure is detected. N is the number of tests. The probability of a failure, p = 0.1. ...
0
votes
2answers
77 views

Little O notation calculus

Imagine we have $a_n(X_n-\theta)-a_n(Y_n-\theta)\xrightarrow[d]{}Z$. Also, $a_n\xrightarrow[]{}\infty$, and $X_n, Y_n\xrightarrow[p]{}\theta$. $o(g(x))$ is an expression that $\lim_{n\rightarrow ...
0
votes
1answer
32 views

Expected Value Intermediate Counting Problem

A palindrome is chosen at random from the list of all 6-digit palindromes, with all entries equally likely to be chosen. (Recall that a palindrome is a number that reads the same forward and ...
0
votes
0answers
38 views

Special case of Kullback-Leibler additivity

I have three random variables $X,Y,Z$. If $(X,Z)$ are an independent pair and $(Y,Z)$ are an independent pair, then the additive property of the Kullback-Leibler divergence says $K(X,Z|Y,Z) = K(X|Y) ...
0
votes
1answer
43 views

Need to figure out how to do the math for deck of cards using different searches.

Below are the two questions I found from the websites ( I have added the link below ), that I am interested in learning the answers. My intention are not to post the answers for that guy but, I ...