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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150 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
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1answer
82 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 ...
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1answer
17 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 ...
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1answer
117 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 ...
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1answer
36 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} ...
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0answers
63 views

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

We have two independent random variables $X_n$ and $Y_n$, where $$X_n=\sum_{i=0}^n x_i$$ and $$Y_n=\sum_{j=0}^n y_j,$$ where $x_i$,$y_j$ are (non-identically) Bernoulli distributed and independent. ...
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3answers
34 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.
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0answers
57 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
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1answer
45 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
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2answers
37 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 ...
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2answers
92 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 ...
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4answers
55 views

A simple question of probability. [closed]

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? $1.np$ $2.pq$ $3.n(1-p)$ ...
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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
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1answer
30 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 ...
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1answer
40 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 ...
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2answers
57 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 ...
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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
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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 ...
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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 ...
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0answers
24 views
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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 ...
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0answers
33 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 ...
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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’. ...
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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 ...
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0answers
38 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 ...
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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" ...
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2answers
42 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
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2answers
76 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
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0answers
46 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 ...
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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 ...
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2answers
42 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. ...
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2answers
79 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 ...
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1answer
38 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 ...
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0answers
41 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) ...
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1answer
45 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 ...
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1answer
45 views

Probability of failure in a machine

I have 18 motors in a thermal power station. If one of the motors "dies" because of the failure of some of the components (for example an injector pin). What is the probability that one of the other ...
0
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1answer
30 views

Board Game Markov Process - Transient Probabilities

I need to write an essay on the Game of Life board game, and so I studied up on Markov Chains to help me calculate the probabilities and average payoffs for the spaces; however I'm not sure whether ...
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1answer
26 views

Distribution of reversed k-th order statistics

Let $X_1,...X_n$ be i.i.d. Let $Y_{(i)}$ the $i$-th order statistic of that sample. The distribution function of the order statistic is given by $$F_{Y_{(i)}}(y) = \sum_{k=i}^n \binom{n}{k} y^k ...
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2answers
132 views

Misunderstanding the Theorem of Bayes

Saw this problem in an article on bbc.com (6 July 2014, "Do doctors understand test results?," by William Kremer BBC World Service; link below, slightly modified): A 50-year-old woman, with no prior ...
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1answer
24 views

Proper formula for this probability

I have here a probability problem that I was able to solve without using any proper formula, i just made it up myself. I wanted to know the proper formula approach for this problem: Amanda has ...
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2answers
43 views

Not sure with my probability understanding

I have here a problem that I am trying to solve but I am stuck somewhere and I am not sure if i am doing it right or not. Erin has some coins in her pockets. In her left pocket she has 1 nickel ...
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0answers
18 views

Confidence size and coverage probability in a confidence set?

Let $\theta \in \Theta \subseteq \mathbb{R^d}$ be the parameter of interest and let $\theta_0$ be the true population parameter value. Let $n$ be the sample size. Let $CS_n$ be the confidence set ...
0
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1answer
33 views

Probability of Random Variable Minus Random Variable

$X_1 , X_4$ ~ $ Binomial(18000,1/6)$. So $X_1+X_4$ ~ $Binomial(18000,1/3)$. I am asked to find $P(X_1-X_4)\leq 80)=?$. The solution is to find $Var(X_1-X_4)=6000$, $E[X_1-X_4]=0$ and then do the ...
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1answer
45 views

Need explanation about probability

I wanted to learn about probability, I have here a sample question that i want to base as my starting point. This was given as our homework but was never discussed in class on how to solve it. ...
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0answers
24 views

A question on probability. Is the question answerable or there is a meta logic issue? [duplicate]

I have the following question and I'm not sure of the right answer (if any), could you help me in elucidating it? If you chose an answer to this question at random, what is the chance you will be ...
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1answer
30 views

Mantel-Haenszel $\chi_1^2$ statistic

I was doing a particular example from the book Epidemiologic Research by Kleinbaum(example 15.6) and didn't understood some basic statistical aspect. ...
1
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1answer
59 views

Is there a fast, reasonably accurate estimator for multinomial PDF?

I am working on a balls in boxes kind of problem, where the probability of a ball ending up in a certain box varies by box, that is, each box has some probability P of getting any ball, all together ...
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1answer
47 views

Geometric Distribution - How to show that a certain event is unplausible?

We have given a geometric distribution with parameter $p$ as well as some result $r$, which we doubt is an outcome of the given distribution. What is the best way to show that $r$ is indeed not a ...
2
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0answers
58 views

Randomness in a sequence

For a function $f$ consider a random sequence $a_{n+1}$ can be either $a_n+f(a_n)$ or $a_n-f(a_n)$ Given that the next term in the sequence is subtracting $f(a_n)$ from the previous term 50% of the ...
2
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1answer
40 views

Expected Payment under limited policy

The unlimited severity distribution for claim amounts under an auto liability insurance policy is given by the cumulative distribution: $$ F(x) = 1 - 0.8e^{-0.02x}-0.2e^{-0.001x} , x \geq 0$$ ...