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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16 views

Problem involving periodic Markov Chains — probability of being in a given state at time $n$

I'm working on the following problem: I believe that the simplest possible irreducible periodic Markov Chain would be one with two states and no self-loops? Does this seem correct? However, I'm ...
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1answer
23 views

Two-group Probability question

I had this question on a test a few days ago, and when I got the test back, this question was marked wrong: In a group of 500 people, 60% of them are female. In this same group, 10% of the people ...
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2answers
47 views

Probability of passing a quiz with random guesses

A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade ...
2
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2answers
40 views

Expected Total Number

To determine whether or not they have a certain disease, 160 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to group the ...
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1answer
29 views

Frequency Distribution and Probability for dependent events

You are playing 3 lacrosse games this week. One game will be on grass and 2 will be on turf; 2 at home and 1 away. Calculate a frequency distribution for the probability of winning at least two of ...
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0answers
17 views

Generalised Poisson Distribution

While studying stochastic processes (specifically the paper http://arxiv.org/abs/cond-mat/0412129v1) I have come across a probability distribution that is a generalisation of the standard Poisson ...
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1answer
21 views

Let X be a discrete random variable

Let X be a discrete random variable. If $E[X]=-3$, then $E[(3+5X)^2]=$ I understand that to find the expected value the formula would be $E[aX+b] = aE[X]+b$ so it would be 3+5(-3). My problem is ...
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1answer
39 views

Probability questions (independent events)

Three people are going to a dinner. the probability that Albertine, Karoline and Patronelle is going is 0.8,0.6,0.9 respectively. a) what is the probability all 3 are going? is this just ...
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0answers
23 views

How to find union and intersection of events?

I have sample space of experiment $S=\left\{x|-\infty<x<\infty\right\}$. I consider events $$A_i=\left\{x \;\middle|\;\frac{1}{2^{i-1}}\le x<\frac{3}{2^i}\right\};i=1,2...$$ And I want to ...
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0answers
15 views

Cumulative Distribution Function in Two Different Circuits [on hold]

Let S be a system composed of two components A and B. Let Fa(t) be the CDF of A at time t and Fb(t) the CDF of B at time t. If I put A and B in serial connection like: ...
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2answers
33 views

What is the probability of rolling $3$ heads before $2$ tails? [closed]

Given that you have a fair coin, what is the probability of rolling $3$ heads before $2$ tails? A thorough walkthrough of this question would be greatly appreciated!
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1answer
36 views

Find conditional probability $\mathbb{P}(X \le x | \max(X,Y)) $

Let $X,Y$ be iid such that $X\sim F>0$ and $Y \sim F>0$ ($X$ and $Y$ have the same probability distribution). Find $\mathbb{P}(X \le x | \max(X,Y)) $. I know that $\max(X,Y) \sim F^2$. I ...
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1answer
19 views

Cumulative Distribution Function applied to exponential variables

Let P be a program composed by two sub-programs that have execution time of T1 and T2 distributed with exponential law of parameters u1 and u2. I have to calculate the Cumulative Distribution ...
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0answers
12 views

Product of conditional probabilities

Should be a simple one here. Basically I am looking for how to re-arrange the following expression: $$( x(t) | Y(t-1) ) | ( y(t) | Y(t-1) )$$ where $x(t)$ is a vector in $R^n$, $y(t)$ is a vector in ...
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0answers
14 views

When can I leave the absolute value from Chebyshev's inequality?

I have a positive random variable which distribution is unkown, but its mean is $10$. I have to find an estimation of its variance, given, that $Pr(X\geq9$)=0.9980 I thought of Chebyshev's ...
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0answers
9 views

Proving $Corr(\hat{e}_{ij}, \hat{e}_{jk}) = \frac{-1}{n_i-1}$ for $ j \neq k$

For the model of a single factor experiment: $y_{ij}= \mu + \alpha_i + e_{ij}$, $(1 \leq i \leq a, 1 \leq j \leq n_i)$, where a = the number of treatments, $n_i$ = the number of experimental units ...
2
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2answers
24 views

Probability Question about Full Houses

So I've figured out the probability of getting a full house. I want to show that P(getting a full house | my first card is the 9h) is the same. Essentially, I want to show that getting a full house ...
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0answers
24 views

Smallest irreducible periodic Markov chain

What would be the smallest periodic Markov chain?
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0answers
70 views

Calculating the probability of letter assignment

We have 10 letters written to 10 different friends and the 10 addressed envelops. The letters are put into the envelops at random, that is, all 10! assignment are equally likely. (a) What is the ...
0
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1answer
19 views

Does the specific bias random coins determines whether functions of these are independent or not?

Consider 3 independent r.v.s $X_1$, $X_2$, $X_3$ that represent the outcomes of three (independent) fair coin tosses. Let 1 denote heads and 0 denote tails. Let two new random variable be defined ...
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0answers
11 views

Weird probability question regarding two states

Say I'm in a swing. Knowing that the two states I could find myself are back and forth, why is $1/2$ a bad approximation for the probability of me being forth ? Why is the probability $>0.5$ for ...
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0answers
21 views

How many strings of 8 heads and tails have at most two consecutive heads? [on hold]

i know the answer, but can someone please do the whole process to explain to me? thank you! in addition, please show me the whole process instead of giving me hints.
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1answer
25 views

Probability of a random triangle containing the center of a polygon

Consider a regular polygon of $2n+1$ sides. Let three random vertices be chosen at random to get a triangle. The probability that the chosen triangle contains the center of the polygon is 5/14. What ...
2
votes
1answer
28 views

Tossing 10 coins on square table

Say we have a table divided into equal squares of length $L$ and $n$ coins of diameter $d<L$. What's the probability that all $n$ coins end up inside some squares after tossing them ? I see that on ...
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0answers
15 views

2 variable with exponential distribution [on hold]

We have $2$ exponential variable $x_1$,$x_2$ $x_1$~Exp($a$) , $x_2$~Exp($b$) (1) $p(x_1>=x_2|x_2>=3)=?$ (2) $p(x_1>=2|x_2>=3)=?$ I have problem for calculating these $2$ ...
0
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1answer
22 views

poker hand: probability of getting 4 cards of equal face value and 1 card of a different value

A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of the following poker hand: Four of a kind (4 cards of equals face value ...
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2answers
54 views

Buffon's needle.

Suppose we have a foor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips? ...
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0answers
22 views

Stationary distribution of a birth-death model where a parameter follows a uniform distribution.

I asked this question about some type a markov process I was interested in. @Did offers an answer but I fail to understand how to apply his answer to a concrete example. I am therefore seeking for an ...
0
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1answer
31 views

How does a Nakagami Random Variable behave?

A Nakagami random variable has the following pdf $$f_{\Omega,m}= \frac{2m^m}{\Gamma(m)\Omega^m} x^{2m-1}e^{-\frac{m}{\Omega}x^2}$$ I have two questions regarding this random variable, 1- Is a sum of ...
0
votes
1answer
18 views

How would you explain this graph illustration of Simpson's paradox?

I need your help for understanding WHAT in the graph you find in the following link proves Simpson's Paradox. For those who don't know about Simpson's paradox, it is the inversion of the inequalities ...
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1answer
13 views

Explanation of this situation with two random variables - $X$ conditionally distributed on $N$?

Let $N$ have a Poisson distribution with parameter $\lambda = 1$. Conditional on $N = n$ let $X$ have a uniform distribution over the integers $0, 1, ..., n+1$. What is the marginal distribution of ...
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1answer
23 views

how many types of events actually exists in the theory of probability?

I read many article on the internet and found that there are only three types of event that can be occurred(or that has been considered in the probability theory). those are : mutually exclusive ...
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3answers
102 views

Betting system for coin toss game?

Is it possible to create a betting system with positive expectancy for a coin toss game. Can we use law of large numbers to create a betting system?
3
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1answer
29 views

Is this argument on positive definite matrices correct?

Let $A$ be a $N\times N$ positive definite matrix. Then, there exists a $N\times 1$ gaussian random vector $a$ such that $A=E[aa^T]$ where $E[.]$ denotes expectation. Then for any given vector $x$, ...
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0answers
25 views

Betting system using law of large number [closed]

Why it is not possible to implement coin toss betting system using law of large numbers? Method such as increasing bet size when we win and decreasing when we loose. If I play 1 dollar initially and ...
0
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1answer
34 views

Coin-flipping experiment: the expected number of flips that land on heads

This question is from Sheldon M. Ross: Introduction to Probability Models which is about finding the expectation by conditioning. Question: A coin, having probability $p$ of landing heads, is ...
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0answers
14 views

Problem in conditional expectation

I came across this problem recently. Let $X$ be a non-negative random variable on $(\Omega,\mathscr{F},\mathbf{P})$ and let $\mathscr{G} \subseteq \mathscr{F}$ be a sub-sigma-algebra. 1) Show that ...
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0answers
27 views

Extinction probability of binomial branching process tends to poisson one.

The folowing is stated and proved in the random graphs book by Luczak, Janson, Rucinski and this is on page 108 in the Giant component section. I can't understand why the conclusion follows from the ...
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0answers
43 views

n bins, m balls and m>n: Probability of at least r bin containing exactly k balls.When bins are numeret from 1…n and ball is equale.

I want to calculate this probability .In this question $N$ bins, $m$ balls: Probability of any bin containing *exactly* $k$ balls. calculate this but I can not understand this calculation.To be more ...
0
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1answer
19 views

A question on semi-martingale and its variations

With probability one, paths of semimartingales have unbounded variation. What I know is that a martingale is also a semi-martingale, for example, Brownian motion. Hence, Brownian is an example of ...
2
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2answers
45 views

What is wrong with my method of finding the probability

One way to solve this and my book has done it is by : This is a well known way, but I have a different method, and it seems logical to me (but I don't know what the mistake is). And yes it's ...
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0answers
49 views

Probability Question - independent events?

Ok, here is the question. An investor Anna owns shares in a stock whose current value is 20 dollars per share. She has decided that she must sell her stock if it goes either down to 5 dollars per ...
1
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1answer
43 views

Rolling a die until I got second 1 or second 2 [closed]

So what is the expected number of rolls until the second 1 or the second 2 appears? I've been calculating for hours but only got a rough feeling that it should be around 7.5. Thanks!
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2answers
34 views

Ball Occupancy Problem

Suppose we put r balls at random in n boxes, i.e., all n r assignments of balls to boxes have equal probability. Let Ai be the event that the ith box is empty and Nn = the number of empty boxes. It is ...
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1answer
52 views

Does $x \perp (y,z)$ imply $x \perp y \mid z$?

Does $x \perp (y,z)$ imply $x \perp y \mid z$, where $\perp$ denotes stochastic independence? I was told it is true and the following is the proof (which I believe is wrong): We want to show that ...
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1answer
23 views

Probability Mass Function, Variance, Expected Value [closed]

This was on a practice exam. I really need help with this question. I already completed 'a' and 'dii' Let X be a continuous random variable with probability density function f (x) = 2x, 0 ≤ x ≤ 1. ...
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0answers
10 views

video lectures on stochastic geometryand point process in wireless communication domain

Can you pls share any link from where i can have video lectures on stochastic geometry with the application in wireless communication. while searching on net i have found some lecture notes in pdf ...
0
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1answer
17 views

Balls with replacement

I have a simple question on drawing balls with replacement. There are 20 red balls, and 10 blue balls, and it is interest in the event that {BBR} where order doesn't matter. So ...
4
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1answer
33 views

Almost equal probable sums with loaded dice

It's known that it's impossible to assign probabilities to a pair of loaded dice so that the sums $2,...,12$ are equally probable. How would one set the probabilities $\{p_i: 1\le i\le 6\}$ and ...
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0answers
8 views

What does the independent statement $(x,y) \perp w \mid y$ mean and what does the “de-generate property” of probability mean?

What does the independent statement $(x,y) \perp w \mid y$ mean? I was guessing that it mean: $$p_{x,y,w|y}(x,y,w \mid \tilde{y})$$ where $y$ and $\tilde{y}$ are not necessarily equal. I interpret ...