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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Problem solving: Counting and probability

i am a little bad at probability, i'm studying to overcome this lack. Since i'm not with a tutor i need some help on the correct way to approach a basic probability problem. I would appreciate your ...
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1answer
67 views

Proving that three events are mutually independent

Suppose that: the events $A$ and $B\cap C$ are independent. the events $B$ and $A\cap C$ are independent. the events $C$ and $A\cap B$ are independent. the events $A$ and $B\cup C$ ...
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2answers
28 views

Conditional probability for random variables with different distributions

Random variables $X$ and $Y$ are independent, where $X$ is exponentially distributed with parameter $1$ and $Y$ has uniform distribution on $[-1,1]$ interval. Find $\mathbb{P}(Y>0|X+Y>1)$. My ...
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1answer
25 views

Combining independent predictions into an overall probability

I am trying to understand the mathematical basis of combining independent probabilities, as described here: http://www.paulgraham.com/naivebayes.html Suppose that being over 7 feet tall indicates ...
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2answers
128 views

A counter example of Brownian Motion

Here is an example in my textbook to illustrate why we need the continuous sample path in the definition of Brownian motion. Let $(B_t)$ be a Brownian motion and $U$ be a uniform random variable on ...
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1answer
21 views

Branching process: Why does the population die or explode?

Consider a population such that each member, independently from other members, at a certain instant of time is replaced by its offspring. Lets denote with $X_n$ $({n\ge 1})$ the amount of the ...
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1answer
34 views

how to compute $E[e^{a^2/2}N^2]$, $N$ is $\mathcal{N}(0,1)$

I have to show that $E[e^{(a^2/2)N^2}]=E[e^{(aNN')}]$ and tell for which values of $a$ these quantities are finite. $N$ and $N'$ are independent $\mathcal{N}(0,1)$ random variables I computed the ...
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1answer
33 views

Finding the variance problem

I am working on the following problem and the explanation was not clear to me, so I am seeking for help. The following is the problem. A fire occurs with a probability of 0.01. The damage Y ...
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1answer
26 views

How to compute this conditional probability in Bayesian Networks?

I met a problem related to conditional probability from the article "Bayesian Networks without Tears"(download) on page 3. According to the Figure 2, the author says $$P(fo=yes|lo=true, ...
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1answer
15 views

expected value product dependent random variables

My question is strictly operative, if I have, for instance, two random variables $X$ and $Y$, $X$ is a $\mathcal{N}(m,\sigma^2)$ and $Y=e^{h(X-m)-1/2(h^2\sigma^2)}$. $E[Ye^X]$ is $\int y e^x p(x) ...
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2answers
29 views

Computing problem in probability theory [on hold]

Josh takes a twenty-question multiple-choice exam where each question has five possible answers. Some of the answers he knows, while others he gets right just by making lucky guesses. Suppose that the ...
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3answers
19 views

What is the probability any one item in a set of 10 items is picked from a pool of 30?

Consider that a set contains 30 distinct items. User must pick 10 distinct items. What is the probability that any given item will appear in the set of items picked? The probability that an item is ...
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4answers
53 views

Probability of drawing a red ball

An urn has $2$ balls and each ball could be green, red or black. We draw a ball and it was green, then it was returned it to the urn. What is the probability that the next ball is red? My attempt: I ...
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0answers
18 views

Overflow and underflow of a probability value

I am evaluating the probability that the minimum of a process is a above a a barrier $\log(H)$. The probability is given by $$P_i=1-\exp\left(-2\frac{(\log(H)-x)(\log(H)-x_b)}{\tau\sigma^2}\right).$$ ...
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0answers
27 views

Normal approximation with dependent variables

I have a sequence of $N$ dependent random variables $$y_i = \frac{x_i}{||\vec x||_2} \quad \mathrm{for} \quad \vec x \sim \mathcal N(0,\mathbb{1}_N),$$ where the $x_i$ are the iid elements of $\vec ...
2
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1answer
21 views

Filtration from a Brownian Motion

The textbook I am reading defines the filtration induced from a Brownian Motion as follows. Let $\{B(t): t \geq 0\}$ be a Brownian Motion defined on some probability space, then we can define a ...
0
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1answer
30 views

Simple conditional probability inequality

I'm reading on some branching process theory in Harris' Theory of Branching Processes and encountered an inequality which looks simple but is eluding me. The full version is a bit complicated to ...
2
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0answers
48 views

Dice: Expected highest value with a tricky condition

I know how to calculate the expected value "E" of a roll of n k-sided dice if we are supposed to keep the highest number rolled. If I am not wrong, the formula is: E = k − (1^n + 2^n + ... + ...
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2answers
37 views

What is p(x=1) of this moment generating function?

So for a MGF like so $M_x(s) = \frac14e^s + \frac34e^{5e^s-5} $ What is P(x=1)? How do I take into account of the 5e^s?
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0answers
15 views

Probabilistic Graphical Model Diagram Notation, what does the box mean?

I'm just learning about probabilistic graphical models, I know the circles represent random variables, shaded being observed and unshaded being latent variables. But what does the box mean?!
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3answers
71 views

Time to $n$ heads when probability is a random variable

I have the following problem. I toss coins until I get a $n$ heads and then stop. The complication is that the probability of getting a head is itself a uniform random variable in the range $[0,1]$. ...
2
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3answers
43 views

Finding the expected value of a function of random variables

I'm having troubles with finding marginal density functions and expected values in my probability theory class. I was hoping someone would be able to walk me through the solution to this question (I ...
0
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3answers
47 views

Fair dice throwing, expected value

We throw a standard fair dice until we threw $5$ and then $2,4$ or $6$ (not necessarily one after another). What is the expected value and variation of number of throws (let it be $X$)? I was ...
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0answers
15 views

Independent Events vs Independent Random Variables

On one of the posts on this site, an OP posed the following question: Given a sample $Y_1, Y_2,\ldots,Y_n$ how do we test if $Y_i$ is independent from the rest of the sample? If the experiment ...
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1answer
16 views

Does the parameter change during data generation in Bayesian Inference?

Let's assume that we have the following graphical model: This graph encodes the joint distribution $P(p,x_1,x_2,x_3,x_4) = P(p)\prod_{i=1}^{4}P(x_i|p)$. In the Bayesian inference, if we know ...
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1answer
54 views

distribution of books among students

There are $p$ students and $q$ books where $q>p$ and all books are different, but each student will get a minimum of $1$ book and a maximum of $(p – 1)$ books. Find the total number of ways of ...
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1answer
35 views

Number of ways to choose 6 cards with the same suit from a normal deck of cards

In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present? One way was $\binom{13}{1}\binom{13}{1}\binom{13}{1}\binom{13}{1}$ but it involves repetition of ...
2
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2answers
37 views

Subset Probability to Element Probability

Is there any way to match (or map) from Subset Propabilities to Element Probabilities? Suppose that John may select x-sized subsets from a population of N items. In every subset he has exactly x ...
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1answer
44 views

Poisson, Gamma distribution example.

Can someone explain me answer for these questions? Suppose customers arrive at a store as a Poisson process with λ = 10 customers per hour. The Poisson process of X ∼ Poisson(λ) the time until k ...
3
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2answers
43 views

Placing a circle in a square lattice

Two part question. Consider the square lattice $\mathbb{Z}^2$: Imagine you are going to place a circle of radius $r$ somewhere in $\mathbb{R}^2$. Question 1: What is the radius of the largest ...
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0answers
21 views

Probability of dice roll (board games)

Assume that we have n * 6side dice. We will roll all n dice. I ask what is a probability of getting at least r * 1(number 1 on a die), s * 2, t * 3, u * 4? Number 6 can be used instead of any of other ...
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0answers
23 views

About independent random variables

Suppose that $\{X_n\}_{n\in\mathbb N}$ are identical distribued and independent random variables with values in $\mathbb Z$. I don't understand why ...
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1answer
26 views

Calculate probability and its accuracy from results of experiments

You have a machine that tells you which of two items weights more than the other. You insert one object in slot 1 and the other in slot 2, press a button and then the machine tells you either "Item in ...
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0answers
31 views

Anybody help me probability and odds [on hold]

1>Bob, Liam and Pedro are competing in a race. a. Draw a tree diagram to illustrate the possible outcomes of the race (first, second, third). b. If they have all had equal records for the season, ...
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0answers
42 views

When can one represent the conditional expectation $E[X|Y]$ as $g(Y)$ with continuous $g$?

Given two random variables $X$ and $Y$ we know that $E[X|Y] = g(Y)$ where $g$ is a Borel function. Is it a good question to ask under which condition there exists a function $g$ which will be ...
4
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1answer
49 views

Uniform sampling with replacement item frequency

Suppose we are sampling from $N$ distinct items uniformly with replacement $M$ times. What can be said about the distribution of frequencies of items drawn? For example, if I sort all the frequencies ...
2
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1answer
54 views

Chance of exactly one birthday out of 336 to be January 1st.

What is the possibility that out of 336 birthdays, exactly one of them is January 1st? I'm assuming not a leap year. This is what I have so far. If we imagine the list birthdays to be a string, there ...
1
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1answer
18 views

What's the probability of a pangram in a crossword occuring by chance?

There are several sources of the percentage occurence of each letter in the English language. So is it possible using these to calculate the probability of a crossword containing each letter of the ...
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0answers
49 views

Is my interpretation of Bayesian probability and inference correct?

I have the following interpretation of the Bayesian probability and inference (without referring to Measure Theory, I am still at the very beginning of learning it): Let's say we have five random ...
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2answers
28 views

Percentage of a quantity

Concrete is sometimes made from 1 part cement, 4 parts blue metal and 3 parts sand. Find the percentage of cement used
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1answer
64 views

stats probability [on hold]

the typical Australian tropical cyclone season 1 November to 30 April averages around 12 tropical cyclones. we assume the prob of arrival of a cyclone is the same for any given month of season a ) ...
2
votes
1answer
33 views

Probability first sample is the smallest in the continuous case

If you take $N+1$ samples independently from a continuous random variable $Y$ with range $[0,1]$, what is the probability that your first sample is smaller than all the others? Let us assume that ...
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votes
1answer
32 views

Derive/ prove: p(a,b|c) = p(a|b,c).p(b|c)

How can this expression be derived? p(a,b|c) = p(a|b,c).p(b|c) where a,b,c are random variables. UPDATE: from the following ...
0
votes
2answers
36 views

Soccer and probability distributions

The USA soccer team is going to play a championship with 7 other tems. The 8 teams, are going to be divided in two groups of 4 each one. From the participants, Brazil is considered the strongest team ...
4
votes
0answers
48 views

Variational formulations in group theory?

I apologise if this is a naïve question. Are there any known / widely applicable / important variational formulations in (finite) group theory? That is, a relationship of the form $$\alpha(G) = ...
0
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1answer
25 views

Calculate P value from Z value

My data consists of values for 192 countries. I want to calculate the outlier value. For this I first calculated the z values for each using the formula for Z scores. Now I want to calculate the P ...
0
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1answer
47 views

Mean and Variance of the Weibull Distribution

The density of the Weibull Distribution is given by: $$f(x) = \alpha x^{\alpha-1}e^{-x^{\alpha}}$$ The Gamma function is defined as: $$\Gamma(\alpha)=\int_{0}^{\infty}x^{\alpha-1}e^{-x} \,dx$$ ...
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1answer
20 views

CD packages probability [on hold]

A company sells CD packages, with 10 CD´s (each package), and you are guaranteed that if a package has more than one defective CD, they will restore you the package. Let $p$ be the probability that ...
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1answer
16 views

Questions about descriptive measures and probability

If $X$ is a binomial random with $n = 10$ and $p = 0.4$, what is the probability that $X$ is greater than $2$? (3dp) As we know the ① $C(n, x)=\dfrac{n!}{x!\cdot(n-x)!}$ ② $P(x)= ...
0
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1answer
46 views

Interesting card game probability question

You have three cards, two of which are the same value (suit does not matter in this game). For example, 9 8 8. You draw six cards in sets of two, and if either of the two cards in a set matches your ...