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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6 views

Easy question: Multiple random variables vs. product of probability spaces

I never had a course in probability theory and the definitions we work with are quite informal, so I am a little bit confused about the difference between "multiple" random variables and the notion of ...
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0answers
10 views

Venn- Diagrams, Probability

I want to know how to draw a Venn Diagram with the given information below.. There are 30 students; 16 are girls; There are 7 girls and 6 boys who have blue eyes. A student is randomly chosen to ...
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2answers
13 views

Probability that an event will occur X times in a row at any point in Y trials?

Event AA has a $60\text{%}$ failure rate. Given $256$ trials, what is the probability that at some point event AA will fail $9$ times in a row? Is there a formula that is fairly plug-and-play? I ...
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0answers
4 views

Expected Probability of a Random Agent and a Probabilistic Agent

I'm running simulations on two agents: random agent and probabilistic agent. The world they are running in is the Wumpus World where the agent is dropped in a 4x4 grid where each cell has a 20% chance ...
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1answer
14 views

Does $E(|X_n - X|) \rightarrow 0$ implies $X_n$ converges in probability to $X$?

I think it does, I've tried proving it by using Chebishev's Inequality but it only prove that it works with quadratic convergence and I can't adapt it... Can you help me please? Thank you very much! ...
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2answers
36 views

Show that $P(X=c)=1 $for some constant c

Suppose $X$ and $Y$ are independent random variables, also $X$ and $X-Y$ are independent. Prove that $$P(X=c)=1$$ for some constant c. I tried using moment generating function, please give me some ...
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0answers
7 views

A joint pdf question

I need help over a question. I appreciate all helps.Thank you.
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1answer
17 views

What is the probability that the engines will allow a safe landing?

Each of the four engines of an airplane are functioning corectly on a given flight with probability of 0.99, and the engines function independently of each other. Assume that the plane can make a safe ...
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0answers
14 views

Strong law of large numbers when sample size is a random variable

For a sequence $X_1, X_2, \ldots, X_n$ of i.i.d. random variables with mean $\mu$, the strong law of large numbers tells us that $$\sum_{i=1}^{n} \frac {X_i} {n} \xrightarrow{a.s.}\ \mu ...
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0answers
14 views

A probabilty of error calculation

Let's assume I have $N$ binary strings $\{T_1,T_2,\ldots,T_N\}$ of length $L$. All these strings satisfy a minimum hamming distance with respect to a reference binary string R with $\|R\|_1$ ones and ...
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0answers
11 views

Kolmogorov zero-one law in continuous time?

Let $(X_t : t \geq 0)$ be a stochastic process. Is it necessarily the case that $$P (\limsup_{t \geq 0} X_t \leq a) \in \{ 0,1\}$$ as it is in discrete time? If some conditions are needed on the ...
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0answers
14 views

Find inequality for gaussian density

Let $C>0$ be a fixed constant. Is it true that $$Cx^2 e^{-x^2}\leq e^{-\frac{x^2}{C}}?$$ More generally, if we have a power $x^p$ in front of the exponential, do we have that $$(C^{1/2}x)^p\leq ...
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0answers
26 views

Derive the expected value of X^0.5

I am doing a question considering a continuous random variable X and have calculated the expected value and variance from the probability density function given. I am unsure of what the expected value ...
0
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1answer
7 views

Probability of getting an outlier in a normal distribution

Given $ N $ data points that fit a normal distribution, what is the probability that the $ N+1^{th} $ data point is further away from the mean of the distribution than the previous $ N $ data points?
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0answers
10 views

In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year. Let X be the number of quakes in a given year. [on hold]

In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year. Let X be the number of quakes in a given year. (a) Justify the use of the Poisson model. ...
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0answers
15 views

recognize the distribution corresponding to this characteristic function

The characteristic function of a random variable X is given as $$\frac{3+cos(t)+cos(2t)}{5} $$, what is the distribution of X? I was thinking of the discrete random variable X=,0,1,2 with mass ...
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1answer
14 views

What is the probability that all are eligible? What is the probability that at least one is ineligible? [on hold]

Past insurance company audits have found that 2 percent of dependents claimed on an employee’s health insurance actually are ineligible for health benefits. An auditor examines a random sample of 10 ...
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0answers
21 views

What is the right probability?

Three men, Abel, Baker and Charlie, are in jail in separate cells and sentenced to death. The governor has selected one of them at random to be pardoned. The guard knows which one is pardoned, but is ...
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0answers
14 views

Lottery probability using hypergeometric distribution

Let's say that we're interested in a "powerball"-type lottery system where five balls are drawn at random and without replacement from an urn containing 25 labeled balls. A players pays $1 to guess ...
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0answers
12 views

Hermite polynomials with non standard variance (not equal to one)

It is known for probabilists that if $p(x)=\frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$ then the derivatives of $p$ can be expressed in terms of the Hermite polynomials as follows: $$\frac{d^n}{dx^n} ...
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2answers
33 views

Probability of a player winning again after i games

I'm in a computer algorithms course and have a question about basic probability. My math background includes no more than discrete math and a little calculus, so this probability question left me ...
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0answers
18 views

joint distribution of two arbitrary distributions?

F = S + E where S: start time and E: execution time, which are arbitrary probability distributions. S and E are discrete and independent.F is finish time of a task which starts in random start time ...
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2answers
92 views

Couple Probability

The problem states that there are 12 boys and 12 girls. Each boy chooses a girl at random and each girl chooses a boy at random. If a boy and a girl choose each other, they form a couple. It then asks ...
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1answer
17 views

Conditional Probability of random variables! [on hold]

X, Y, Z are i.i.d continuous random variables. How can I compute (1) P(X>Y|X>Z) (2) P(X>Y|Y>Z) ? It seems to be easy but at the same time, confusing! Help me. Thank you:)
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0answers
13 views

Conditional probability of university selection [on hold]

From a group of candidates, 25% are not suitable for the University admission. As the result of selection process only 75% of these unsuitable students are rejected. Overall 50% of students are ...
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1answer
10 views

Type II error with Poisson Distribution

I am having a lot of trouble figuring out how to go forward with this one, though I feel like it should be pretty easy (it's been a long day). This is for a homework problem, and it's set up like ...
3
votes
2answers
21 views

What is the expected value of the mean of the highest $m$ numbers in a population of $N$ normally distributed random variables?

Suppose that I randomly generate $N$ numbers according to the standard normal distribution, $\mathcal{N}(0,1)$. Then suppose I pick the highest $m$ numbers, $x_1\leq x_2 \leq \cdots \leq x_m$. ...
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0answers
15 views

Partition in graph connecting itself and other half

Let $G=(V,E)$ be a graph with $n$ vertices and minimum degree $\delta>10$. Prove that there is a partition of $V$ into two disjoint subsets $A$ and $B$ so that $|A|\leq ...
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1answer
19 views

Could not find right formula for Conditional Probability [on hold]

P(A) = 0.20 P(B) = 0.62 Assuming that A and B and mutually exclusive, the conditional probability $P(A|B^c)$ is equal to... A) 0.769 B) 0.797 C) 0.948 D) 0.526 I've tried all the formula but I ...
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0answers
11 views

Bound on difference of two i.i.d. variables [duplicate]

Prove that for every two independent, identically distributed real random varaibles $X,Y$, $$Pr(|X-Y|\leq 2)\leq 3\cdot Pr(|X-Y|\leq 1)$$ [Source: The probabilistic method, Alon and Spencer]
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1answer
22 views

Estimating the missing points of a 3D point cloud

Consider a cloud of N points (forming a smooth 3D object), in which n points are missing. Also, consider that there is no prior knowledge about the original shape of the point cloud. The only ...
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1answer
14 views

Probability of sequential successes

I've looked around and seen some similar questions, but none that seems to exactly anwer my question, and rather than resurrect old, possibly-related, questions, I thought I'd start a new one, so here ...
1
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1answer
36 views

$X_n$ are r.v.s, is it true that $E[\sum_{n=1}^{\infty} X_n] = \sum_{n=1}^{\infty} E[X_n] $?

$X_n$ are r.v.s, is it true that $E[\sum_{n=1}^{\infty} X_n] = \sum_{n=1}^{\infty} E[X_n] $? My feeling is that this is not necessarily true. But cannot come up with an example. Can someone provide ...
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0answers
9 views

Prove that expected value is a limit of generic function

How can I show that for random variable $X$ which is descbribed by generating function $g(x) = \sum_{n\geq 0} x^nPr[X=x]$ holds $$EX = \lim_{x \rightarrow{1^-}} g'(x)$$
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0answers
28 views

Calculating Map estimate [on hold]

Hello everyone I am stuck on this problem: Given N independent measurements from an experiment that generates exponentially distributed random variables: $$f(x)={1\over y}e^{-x\over y}$$ ...
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1answer
25 views

Probability that it will rain 2 consecutive days? How?

so it's a pretty simple question but I am stumped, help anyone? The first question was: i. Find the probability that it will rain on any particular day in August. ^We are given the mean number of ...
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1answer
22 views

Applying the Poisson Distribution to problems

The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of $3$ accidents per year. Find the probability that more than one year ...
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1answer
11 views

Finding conditional probability from the joint PMF

I have no idea how to get tabular to work on here so the table isn't rendering. A joint PMF $p_{X, Y}[i, j]$ has the values shown in table. Determine the conditional PMF $p_{Y|X}$. Are the random ...
-1
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0answers
29 views

The two envelopes paradox

I have the following problem: Two envelopes, each containing a check, are placed in front of you. You are to choose one of the envelopes, open it, and see the amount of the check. At this point you ...
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0answers
21 views

Negative Correlation and Securities?

The following is a problem in the textbook I am trying to do as I practice for an exam. I would appreciate some help on this question I have completed part a. I have determined expected return in ...
3
votes
1answer
15 views

Distribution of numbers $n = \max(x, y)$ where $x, y$ are random numbers between $0$ and $1$

I define a function $$f = \max(\mbox{rand}(0, 1), \mbox{rand}(0, 1))$$ such that $f$ returns the maximum (greater number) of two random selected numbers between $0$ and $1$. Plotting a histogram for ...
2
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2answers
21 views

Covariance for equal variances

If X and Y are independent random variables with equal variances, find Cov(X+Y, X-Y). I am confused on how to do this? I feel like I am over thinking this question.
1
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1answer
15 views

How Do I Find The Permanent of a Double Stochastic Matrix n * n size

I am reading a book on Stochastic Models, and I don't understand this practice questions: A doubly stochastic n × n matrix S has all entries equal to 1/n. The permament of a n × n matrx A is ...
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1answer
14 views

Find the distribution of how a drunkard is walking

I have another homework question, and part of it is throwing me for a loop. The question is (paraphrased): A drunkard starts at position 0, and takes either one step forward (with probability p) or ...
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2answers
10 views

Variance & Joint Density Function

$X$ and $Y$ have joint density given by $$f_{XY}(x,y)=\begin{cases}2,& 0≤x≤y≤1 \\0,& \text{elsewhere}\end{cases}$$ a) Find $\text{Var}(Y|X=x_0)$. b) What is the answer if $x_0$ is not in the ...
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1answer
18 views

Finding the distribution of $Y_2$,knowing that $Y_1 \in Po(\lambda/2)$

The random variables $N,X_1,X_2..$ are independent, $N\in Po(\lambda)$, and $X_k \in B(1/2) , k \geq 1$ Set. $Y_1 =\sum\limits_{k=1}^{N}X_k $ and $Y_2 = N - Y_1$. Determine the distributions of ...
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0answers
24 views

How to divide set of numbers [on hold]

$A = \left\{a1, a2, \ldots, a_N\right\}$ is a set of $n$ numbers elements (positive integers) and must be divided into $K$ subsets in order so that the sum of all elements in each subset are equal to ...
0
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2answers
14 views

Dependence of random variables

I need to solve the following problem: Let X be a normal random variable with mean  and standard deviation  and let I, independent of X, be such that P{I = 2} = P{I = -2} = 0.5. Let Y = I X. In ...
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1answer
10 views

One parent is a cystic fibrosis carrier, and the other has no cystic fibrosis gene

One parent is a cystic fibrosis carrier, and the other has no cystic fibrosis gene. Find the probability of each of the following. (a) The child would have cystic fibrosis. Answer = 1/4 = 0.25 (b) ...
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3answers
32 views

P(A|B^c) given the following

Given $P(A) = 0.2, P(B) = 0.6$, where A and B are mutually exclusive, find the conditional probability $P(A|B^c)$. How do I determine this answer? I've been trying to figure it out for hours.