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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1answer
53 views

locally linearize a CDF

I have a sequence of discrete CDF's that converge to continuous CDF. Assume we call it $F_n(x)$. If say at some point, say $R$, $F_n$ is differentiable, then we can write $F_n(R+\xi) \approx ...
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1answer
64 views

Estimate the probability using Markov chains

please consider this question: A study using Markov chains to estimate a patient's prognosis for improving under various treatment plans gives the following transition matrix as an example ...
2
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1answer
33 views

Conditional Probabilities and non-zero condtions

When working with conditionals $\mathcal{P}(A \mid B)$ do we have a proof obligation to show that $\mathcal{P}(B) \neq 0$ ? In-particular, what about in the expression, $\mathcal{P}(A \cap B) = ...
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1answer
48 views

What's the probability 2 people sharing a house will get the same disease?

I am interested in environmental causes for illnesses. Suppose an illness has a prevalence of 0.1% of the population. What's the probability then that 2 people who share the same house will both get ...
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1answer
23 views

Question about normal distribution statistics

I am doing a project about descision analysis, but I don't understand one crucial step in my book. F(x) is the standard normal cumulative distribution function, and we have: $$F(x) = 0.744$$ From ...
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0answers
73 views

Why does it exist?

I can show that $\lim_{a \rightarrow \infty} \int_{-\infty}^{a} (\cos(tu)-e^{-\frac{t^2}{2}})e^{-\frac{u^2}{2}}du$ converges to 0 but I am not sure why this implies the convergence of $$\lim_{b ...
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0answers
24 views

Find x, when F(x) is a cdf with given mean and std

I have a small question. For a problem in desicion analysis course, I come to the equation F(x) = 0.8 where X is distributed with mean 50 and standard deviation 10. How can I find x? (my probability ...
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1answer
150 views

Probability of X winning N number of games

Say there is a player X. X has to choose and play one of the 4 games - Game A, Game B, Game C, Game D ...
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2answers
48 views

Probability problem and number theory

A standard fair 6-sided dice is rolled $n$ times. Let $X_k$ be the spot which faced up inthe k-th round. What is the probability that $X_1+X_2+...+X_n$ is divisible by 7? I tried to solve it by ...
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2answers
387 views

Probability Of Rolling A Strictly Increasing Sequence On A Six-Sided Die

By rolling a six-sided die 6 times, a strictly increasing sequence of numbers was obtained, what is the probability of such an event? I have no ideas on how to attack this. It says, an ...
0
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1answer
29 views

Does $E(X|\min(X,k))$ converges to $X$ in $L^1$ or almost surely or neither?

$P(X=k)=1/(2^k)$, $k=1,2,3... ~~~ Y_k=E(X|\min(X,k))$ Does $Y_k$ converges to $X$ in $L^1$ or almost surely or neither? Can somebody give a proof?
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2answers
120 views

Asymptotics of probability of Newton-Pepys problem

In Newton-Pepys problem one is interested in probability $p_n$ of getting at least $n$ sixes in $6 n$ independent throws of regular 6-sided die. The number of sixes $S_m$ obtained in $m$ throws ...
1
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1answer
46 views

Mixed Distribution Problem

You design an insurance policy that pays a random amount Payment $= 1000 \cdot A$, where $A$ denotes the age at death. $A$ is assumed to have a continuous uniform distribution on $[50,110]$ (that is, ...
0
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1answer
31 views

What are those random variables' distributions?

$X_1,X_2....X_n$~Norm($\mu,\sigma^2$).What are the distributions of those random variable that is following:1.$Y_1=\frac{X_1-X_2}{\sqrt{X_3^2+X_4^2}}$2.$Y_2=\frac{\sqrt{n-1}X_1}{\sqrt{\sum_{i=2}^n ...
3
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1answer
36 views

a method for solving a problem in probability [closed]

If the probability that the man aged $60$ will live to be $70$ is $0.65$, what is the probability that out of $10$ men, now $60$, at least $7$ will go up to $70$?
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1answer
180 views

What does it actually mean by max or min of a random variable?

I've been looking trough Google for getting the answer, yet still I haven't found the exact meaning of it. What does it exactly mean that one wants to evaluate $max$ or $min$ of a random variable? I ...
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2answers
60 views

a problem of probability involving positive integers

The question is as follows :- Two integer 'a' and 'b' are randomly selected from the set ${1,2,.....}$ (with replacement) then prove that probability of $(a^2 +b^2)/5$ being positive integer is ...
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2answers
190 views

How to handle dependence in a probabilistic ball problem?

I am learning about how to handle dependence when doing probabilistic calculations and I came across this problem I don't understand how to solve. I am given $10$ colored balls painted either red or ...
0
votes
1answer
41 views

Integration of density function of x+y

http://imgur.com/X48xBhj I don't understand how $$ \int_0^1 f_x(a-y)dy $$ equals to $$ \int_0^a dy $$ Also how you know to integrate from a-1 to 2 equals to 1< a < 2.
0
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1answer
69 views

Probability of getting same number of black and white pebbles

I am trying to learn some probability and the following problem summarises my current confusion quite well. Any help is gratefully received. I have $n$ pebbles, some of which are black, some white ...
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3answers
388 views

How many books are in a library?

My cousin is at elementary school and every week is given a book by his teacher. He then reads it and returns it in time to get another one the next week. After a while we started noticing that he ...
3
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0answers
72 views

Probability that array remains the same after k swaps as per pseudocode in description [closed]

Consider this pseudocode: int arr[N]; for(int i=0;i
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1answer
44 views

Show that the rv $X = -X$

Let $X\in N(0,1)$ and show that $X=-X$ (equal in distribution) I assume that I need to use the distribution function for the standard normal probability density. So we have: ...
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2answers
193 views

Probability of poker cards using combinations, its a poker question [closed]

Choose two cards from a regular 52 card deck, what is the probability of getting atleast one face card from the two card hand drawn? (Without replacement) What is the probability that the first card ...
8
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1answer
267 views

What is the intuition behind the generalized confidence interval?

What is the intuition behind the generalized confidence interval? My best description on GCI that it is the way to derive a formula to calcuate the area of the center region in a asymetry distribution ...
2
votes
1answer
140 views

Multivariate Gaussian decomposition

I've seen around the claim that an $n$-dimensional Gaussian random variable (say, having unit covariance) can be decomposed into the product of two independent random variables. $$U=ZS$$ where $Z$ is ...
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2answers
34 views

probability Case

Dears I've the below probability case There are 20 teachers in a university. Eight (8) of them specialize in algebra, 5 in district Mathematics, 4 in physics and 3 in Geography. How many ways we have ...
0
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1answer
23 views

Probability Differentiation

http://i.imgur.com/nl3bCrt.png I don't understand how $$F_X(y^{\frac{1}{n}}) $$ is equal to $$ y^{\frac{1}{n}} $$ and when you take the derivative to get the density function shouldn't it be $$ ...
4
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2answers
250 views

Chance of adjacent lockers with the same combination

One weird thing that happened to me in high school was that the combination lock on my locker had the exact same combination as the locker next to it. It always struck me that the odds were crazy on ...
0
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1answer
41 views

Given a distribution to generate a set of numbers, what is probability of generating two consecutive numbers whose difference is greater than k?

Suppose I am generating a set of numbers {$x_1$, $x_2$, $x_3$ ... $x_n$} from a given probability distribution $f(x)$. Is it possible to calculate the probability of finding $x_{i+1}-x_i \geq k$, ...
1
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2answers
43 views

Integration of the product of probability densities

Does a probability density $f(x|\alpha)$ multiplied by another probability density $g(\alpha)$ , where of course both integrate to one, also integrate to one if we integrate with respect to $\alpha$? ...
0
votes
1answer
50 views

Trouble Understanding a Problem

http://imgur.com/37FG64q I don't understand how the normal random variable with parameters 0,1 equals (x-mu)/sigma=Z ~ N(0,1). If I plug that into the pdf of the normal distribution I get ...
1
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1answer
54 views

Find $\mathsf{E}\left[(X_1+X_2)^4\mid X_1-X_2\right]$ where $X_1$ and $X_2$ are iid standard normal

Find $$\mathsf{E}\left[(X_1+X_2)^4\mid X_1-X_2\right]$$ where $X_1$ and $X_2$ are i.i.d. standard normal. I know that both $X_1+X_2$ and $X_1-X_2$ are both distributed $N(0,2)$. I'm having trouble ...
1
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0answers
51 views

Reputation probabilities

Is there a probabilistic model for what one's reputation can be on MSE? I can of course obtain increments of points in +2, +5, + 10, + 15, +50, +100. Are there models for what my reputation will ...
9
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2answers
266 views

An extrasensory perception strategy :-)

Inspired by classical Joseph Banks Rhine experiments demonstrating an extrasensory perception (see, for instance, the beginning of the respective chapter of Jeffrey Mishlove book “The Roots of ...
4
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4answers
251 views

Probability that a geyser erupts

Lets say you have a geyser that has a 2/3 probability of erupting in a 50 minute interval? What is the probability that it will erupt in a 20 minute interval? The way I tried to solve it that ...
0
votes
1answer
37 views

Generate random numbers from a family of PDFs

For a part of a simulation task, I need to generate (lots of) random numbers from the distribution $$P(E_k | N) = \frac{1}{E_k}\left(\frac{E_k}{k_BT}\right)^{N-1}\frac{1}{(N-2)!} e^{-E_k/k_BT} $$ ...
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0answers
58 views

How does one approximate $P(\sqrt{X_1} + \sqrt{X_2} + … + \sqrt{X_n} \leq x)$?

Given Problem Let $X_1, X_2, ..., X_n$ be independent, normally distributed random variables having mean $0$ and variance $\sigma^2$. How should $P(\sqrt{X_1} + \sqrt{X_2} + ... + \sqrt{X_n} \leq ...
2
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1answer
75 views

expected value of a function of two random variables

I am trying to calculate this sum (which is expected value of a function of two independent Poisson random variables): ...
2
votes
1answer
94 views

Probability of choosing a partner

My problem is: There are 10 boy and 10 girl and we choose couples(boy-girl) randomly. We know 3 guys (Aladar,Bela,Csaba) and 3 girls (Aranka,Bori,Cecilia). What is the probability that Aladar is not ...
2
votes
2answers
138 views

What type of Probability distribution is best for this problem?

An auto insurance company is implementing a new bonus system. In each month the policyholder does not have an accident, he ore she will receive 5.00 cash back bonus from the insurer. Among the 1000 ...
1
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1answer
273 views

Calculating probability of exceeding fixed Hash table bucket chain depth

I'm attempting to create a Hash table in hardware and I would like to calculate the optimal table size and chain length (for collisions). Unlike in software, I can't easily (and don't want to) grow my ...
3
votes
1answer
82 views

Curious graph: expected number of balls in the $i$th ordered bin

$k$ balls are uniformly and independently placed into $n$ bins. Sort the bins in ascending order. Is there a general formula for the expected number of balls in the $i$th ordered bin? I don't really ...
0
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1answer
50 views

Extreme Value Distribution

I would appreciate a lead\tip on the next one: Z is a standard random variable from the extreme value distribution. I need to show that $Y=\sigma \cdot Z+\mu$ is an extreme value variable with ...
3
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1answer
83 views

How to find $P(X=r)$ from probability generating function of $X$?

I have a probability generating function $$G_X(s) = \frac{p+ps}{1-s+p+ps}$$ and I need to find $P(X=r)$. How do I get this from the probability generating function? I was thinking about finding ...
0
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2answers
336 views

Probability of a player scoring multiple goals in a match

I'm struggling to work out this answer. Say Team A is estimated to score $1.6$ goals in a match and Team B is estimated to score $1.1$ goals. Team A's striker is expected to score 40% of his team's ...
0
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1answer
58 views

Sampling without replacement

I've recently started studying statistics again, and I've just come across sampling without replacement. My book states that if we have a elements of type I and b elements of type II, then the ...
0
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1answer
57 views

Probability that Davis got 3 Souvenirs

Davis likes baseball games. Suppose there are a 100 souvenirs in one of the games and 4936 fans that attend. Calculate the probability that Davis receives 3 souvenirs. What I did was I used a ...
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2answers
164 views

Probability of every coin displaying HEAD if a coin is tossed 12 times

What is the probability of every coin displaying HEAD if a coin is tossed 12 times. Is it $\frac{1}{12}$ or $\frac{1}{1024}$?
1
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1answer
330 views

Elevator stop, other approach

There is a $10$-floor building, $10$ people get in the elevator in the ground floor and each gets off at one of the floors randomly and independently. What is the probability that the elevator stops ...