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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111 views

Expected number of targets hit by 10 shooters, 2 bullets each, 20 targets

Consider a competition with 10 clay shooters. Each shooter has equal ability and they all use identical shotguns. Each shotgun is loaded with two bullets, therefore each shooter can shoot twice. ...
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2answers
54 views

6 Professors and 8 floors - expected value

I have this problem I need help with. There are 6 professors on an elevator that has 8 floors/stops. Each professors exits the elevator randomly(1/8 chance). What is the expected value E(X) of stops ...
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1answer
38 views

Difference between $\lim P[…]$ and $P[ \lim ]$

In a Galton-Watson branching process the extinction probability is sometimes given by $$\lim_{t \rightarrow \infty} P[X(t)=0]$$ and sometimes as $$ P[\lim_{t \rightarrow \infty}X(t)=0]$$ Is there a ...
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1answer
66 views

Conditional Probability using a Matrix

I understand how to find P1: that is simply: P(D1|D0)=0.8 P(W1|D0)=0.2 P(D1|W1)=0.4 P(W1|W0)=0.6 I do not however, understand how to find P2 using the matrix. Normally I would solve it as ...
2
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1answer
147 views

Relation between uniformly distributed random variable and i.i.d Bernoulli sequence (Cantor space)

(Uniform RV <==> i.i.d Bernoulli sequence) (1) Let $(X_n)_n$ be a sequence of i.i.d. Bernoulli random variables($P(X_n=0)=P(X_n=1)=\frac 12$) on a probability space. Then show that $\xi:= \sum_n ...
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0answers
24 views

Mathematics branch concerned with availability of information

Is there a branch of mathematics that study about availability of information? For example, if I want to search for something on the internet, is there a branch of mathematics that can predict how ...
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0answers
33 views

Probability that coworkers won't complain

I am an anesthesiologist in a group of 26 total. We have 19 of our members working Monday through Friday. We always have complaints from our members about their work assignment. I wondered if ...
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1answer
29 views

What is the variance of multiple indicator random variables?!

Consider the following independent random variables $(V_1,V_2,V_3,\ldots,V_n)$ and a random variable $X$ as a function of these other random variables defined as follow on a set $A=(-\infty,x]$: $$ \ ...
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2answers
37 views

Proving the Probability of an Event Through Bayes Theorem.

The question goes as such: An event A can occur if only one of the mutually exclusive events B1, B2, or B3 occur. Show that P(A) = P(B1)P(A|B1)+P(B2)(A|B2)+P(B3)*(A|B3) my working out: P[A|(B1 U B2 ...
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1answer
72 views

Probability, exponential distribution [closed]

The time until the failure of a hard-disk component is exponential distributed with a mean of $400$ days. a. What is the probability that a hard-disk component will fail within $200$ days? b. The ...
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0answers
44 views

Sampling and averaging in Monte Carlo Simulation

(First of all, I apologize for the vague title. Couldn't think of rather proper one.) Let's say that we have 10 items where each item has probability distribution of one's own, say Lognormal ...
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1answer
79 views

Errors are known to occur in 0.9% of hard disks. In a sample of 5 hard disks, what is the probability that 4 or more are found to be error-free?

Hard disk error is most common non-accidental cause of data loss. A large company checks a random sample of its computers each month for hard disk errors. Errors are known to occur in $0.9\%$ of ...
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3answers
90 views

A fair coin is tossed 100 times. What is the probability that more than 55 heads are observed? [closed]

A fair coin is tossed 100 times. What is the probability that more than 55 heads are observed? I need a clarification on how to use binomial distribution formula in this problem. What i got was: ...
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1answer
26 views

Given a set of partial orderings of samples from a set of distributions, can we estimate the (relative) mean of the distributions?

This problem is motivated by attempting to construct a total ordering out of an arbitrarily large set of potentially contradictory partial orderings. Let's assume we have some set of items I for ...
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1answer
38 views

Expected Value of a mixed distribution

I have a question from my practice actuary exam... I understand one method of arriving at the answer, however the alternative method is giving me a bit of confusion! I have the lifetime of seismic ...
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0answers
33 views

Probability of cryptocoin mining pool payout?

I find probabilities incredibly interesting, but the methods used by cryptocoin mining pools have too many variables for me to make sense of. I'm a bit of a layman, so be easy on me. I'm hoping that ...
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1answer
59 views

solving a simple inverse problem related to elliptic pde

Suppose that I have the elliptic PDE $\nabla(\nabla A(x)\cdot U(x)) = 0$ where $x \in [0,l_1]\times [0,l_2]$ with boundary conditions $U(0,x_2) = 0, U(l_1,x_2)=1$ and $U_{x_1}(x_1,0)=0, ...
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4answers
105 views

Probability of drawing at least 1 red, 1 blue, 1 green, 1 white, 1 black, and 1 grey when drawing 8 balls from a pool of 30?

Given a pool of 30 balls (5 of each color). When drawing 8 balls without replacement, what is the probability of getting at least one of each color? Related: Probability of drawing at least one red ...
0
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1answer
370 views

expected value for the number of rolls of the dice until getting a 6 with a max of 10 trials

Suppose that we roll a fair die until a 6 comes up or we have rolled it 10 times. What is the expected number of times we roll the die? My answer: The ith roll of the dice may give a 6 where ...
1
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1answer
22 views

Moment-determinacy in multivariate case

Let $X$ be a random vector with probability density $p$. In the scalar case I have learned that if the characteristic function of $X$ is real analytic, then all moments exist and $p$ is determined ...
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2answers
50 views

Marginal distributions of a random vector

I have the random vector $(X,Y)$ with density function $8x^{2}y$ for $0 < x < 1$, $0 < y < \sqrt{x}$ I am trying to find the marginal distributions of $X$ and $Y$. For $X$ this seems to be ...
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4answers
46 views

What is the probability that a person has both of these attributes?

The probability that a blue-eyed person is left-handed is $\frac{1}{7}$. The probability that a left-handed person is blue-eyed is $\frac{1}{3}$ . The probability that a person has neither of the ...
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2answers
36 views

What is the probability that the 3 remaining cards of the suit are in one player's hand?

A standard pack of 52 cards with 4 suits (each having 13 denominations) is well shuffled and dealt out to 4 players (N, S, E and W). They each receive 13 cards. If N and S have exactly 10 cards of a ...
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2answers
156 views

Finding the mean and variance of an exponential probability distribution

I'm taking a probability theory course, and I'm struggling a bit with gamma and exponential distributions. Here's a question that I'm stuck on: The length of time Y necessary to complete a key ...
2
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1answer
72 views

Infinite Tree Probability Question

Suppose I have 10 dollars and I'm able to make fair 50/50 bets like flipping a coin. Now suppose each bet is for 1 dollar. What is the probability that if I keep making bets until I hit 0 dollars ...
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2answers
42 views

What is the probability that no two married members sit next to each other?

A dancing club consists of 24 people (12 male and 12 female); out of the 24 people, there are five married couples. If the members of the club sit in a row randomly, what is the probability that no ...
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1answer
20 views

Conditional probability in family

Assume that a family has four children. The probability of having a boy is p, and the genders of children in a family is assumed to be independent. Now, if we know that the eldest is a boy, the ...
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0answers
118 views

calculating roulette wheel selection probabilities with reverse fitness function (genetic algorithm)

i am trying to calculate the probabilities for a roulette wheel selection operator for a genetic algorithm and i am having a little bit of trouble getting my head around how to do it with a fitness ...
1
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1answer
30 views

Limit justified by monotonicity of 2 sides

P. 40 of Probability with Martingales by Williams reads: $P(\bigcap\limits_{n \geq m}E_n^c) = \prod\limits_{n \geq m}(1-p_n)$ "this equation being true if the condition $\{n \geq m\}$ is replaced by ...
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2answers
56 views

Transforming two independent variables, probability

Let $U$ and $V$ be independent variables. Let $V$ be uniformly distributed on interval $[-\pi, \pi]$ and let $U$ be exponentially distributed with pdf $f(u) = \lambda e^{-\lambda u}$. Let $(X,Y) = ...
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1answer
32 views

How to check hypothesis in statistical data?

I have a statistical problem. In a city there are some hostels which differ by the number of rooms. The input data are the following. In a table there is information about hostels and corresponding ...
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0answers
26 views

Secretary problem *without* each ordering equally likely

Also known as: the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. See http://en.wikipedia.org/wiki/Secretary_problem $n/e$ is ...
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0answers
27 views

kullback liebler divergence for correlated processes

Suppose $X_n^{(1)}=\lambda_1 X_{n-1}^{(1)}+\mu_1+\epsilon_n^{(1)}$ and $X_{n}^{(2)}=\lambda_2X_{n-1}^{(2)}+\mu_2+\epsilon_n^{(2)}$ where $|\lambda_i|<1$ for $i=1,2$ and $\epsilon_n^{(i)}$ are ...
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2answers
58 views

GRE - Pobability Question

One person is to be selected at random from a group of 25 people. The probability that the selected person will be a male is 0.44, and the probability that the selected person will be a male who was ...
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2answers
95 views

Expectation of maximum of iid random variables

Let $X_1, X_2, \ldots, X_n$ be independent random variables having the common density function $f(x)$. We have $$f(x) = \begin{cases} 1 & \text{for } 0 < x < 1, \\ 0 & \text{otherwise} ...
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1answer
30 views

Bivariate Normal probability question

I have this homework question Suppose $(X,Y)\sim BN(u_x=0,u_y=0,w_x^2=1,w_y^2=1,p=-0.6)$. Find: a) $c$ such that $8X+10Y$ and $cX+5Y$ are independent b) $P(X<0,Y>0)$ My thoughts are (a) ...
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0answers
15 views

Time required for maximum number of randomly spawning objects given constraints

Some info about the problem: The objects will be spawning on a square ring like this. This ring is to scale, its dimensions are 44x44 on the outside and 40x40 on the inside. The objects are 2x2 and ...
1
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1answer
82 views

A nonnegative random variable has zero expectation if and only if it is zero almost surely

Let $Y$ be a non-negative random variable. Prove that $E(Y) = 0$ if and only if $P(Y=0)=1$. My understanding is that while you can prove it for discrete Y, the result is true for all Y.
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3answers
305 views

Minimum number of attempts to guess a PIN code, given constraints

I'm playing a video game at the moment called Sleeping Dogs, in which some of the mini-missions are to 'hack' a security camera, by guessing a four-digit PIN code. Here are the rules: 1) You are ...
1
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2answers
60 views

Probability of drawing at least one red and at least one green ball.

Given a bag containing 10 red balls and 10 green balls. When you draw 6 balls, without replacement, what is the probability that you will have at least 1 red and 1 green ball. I attempted this ...
0
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1answer
48 views

Calculating the chance of something happening over and over again

I'm trying to calculate the probability, and potential cost on society, of people returning to homelessness after going through the system one, two, or several more times. Let's say that someone who ...
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0answers
32 views

Sum of function applied to parts not equal to function of total

The general goal is to determine the effectiveness of the test pill's ability to keep the test subjects from getting sick using the following data. | Test Subjects | Took Test Pill | ...
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0answers
45 views

Sum of independent discrete random variable

Here is my attempt of deriving the sum of independent random variable in the discrete case : $\underline{\textbf{Sum of independent random variables}}$ Let $\mathcal{C_1}, \mathcal{C_2}$ be ...
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0answers
17 views

Weighted probabilities assigned to a two stock portfolio

Does anyone know how to input a two variable portfolio with uneven weighted probabilties into an HP10bii+? By uneven I mean the weightings are not in increments of 10% and thus you can't simply equate ...
2
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2answers
126 views

If I randomly throw 10,000 balls to 4,000 buckets, what is the probability that at least one bucket contains more than 10 balls?

If I randomly throw 10,000 balls to 4,000 buckets, what is the probability that at least one bucket contains more than 10 balls? I don't know how to even approach this. A rough number is also ...
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0answers
84 views

Transformation of variables

Let variables $U$ and $V$ be uniformly distributed on $[-\pi, \pi]$, and independent. Let: $$(x,y) = (\cos(U+V),\sin(U-V))$$ What is the probability distribution function of $f_{x,y}(x,y)$ My ...
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1answer
27 views

(Multidimensional) Standard Brownian Motion: Convergence

Relating to this question, I have a further one, and hope, someone can help me. I know that $$\left(X_j - X_{j-1}\right)_{j=1}^t \xrightarrow{d} \left(Y_j\right)_{j=1}^t.$$ Further, we know that ...
1
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1answer
53 views

Basic probability limit problem

Let $g(x)$ be a smooth probability density function, whose mean value is $0$. The variance of $g(x)$ is finite, and $\forall x\in R\ \ g(x)>0$. Under the above conditions, does the following ...
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1answer
42 views

how to compute the distance between a matrix and its lower rank approximation?

I have a matrix $X$ and $Z$ a lower rank approximation of $X$ obtained using only few of the columns of $X$. I would like to have a measure of how distant are $X$ and $Z$. In particular I would like ...
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4answers
35 views

Dice probabilities, $2$ of $3$

What is the probability that at least two of three dice will roll a three or higher? There must be an equation that would allow one to expand this to any number of dice.