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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75 views
Difference and relation between dependency graph and graphical model?
From page 2 of
http://www.mpi-inf.mpg.de/departments/d1/teaching/ss11/ProbMethod/files/lll.pdf
Let $A_1 , A_2 , \dots, A_n$ be $n$ events on a probability space $Ω$.
The dependency graph is a ...
1
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1answer
551 views
Tree Diagram Probability [duplicate]
Possible Duplicate:
In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
I have a question for practice:
Imagine that you ...
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0answers
52 views
Two definitions of independence of an event and a set of events
I found there are two definitions for independence of an event and a set of events for Lovasz local lemma.
From page 3 of a note
An event $A$ is said to be independent of a finite ...
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2answers
79 views
Binomial Distribution
I'm trying to solve this question, but since I missed the lecture I'm not where to start, and looking online doesn't help.
Can someone show me how to answer:
Given that X has a binomial ...
2
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1answer
234 views
Probability: Picking 2 different colored balls from 2 urns without replacement
Urn 1 contains 4 red chips and 3 white chips. Urn 2 contains 3 red chips and 2 white chips. 2 chips are chosen at random and without replacement from each urn. 1) What is the probability that all 4 ...
1
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2answers
103 views
Probability mass function and conditional probabilities
If $p_X(k)$ and $p_{Y|X}(y|k)$ are given, how can we calculate $p_Y(y)$? We cannot assume that $p_Y(y)$ and $p_X(k)$ are independent.
I know that $p_X(k) \cdot p_{Y|X}(y|k) = p_{Y,X}(y,k)$ but how ...
2
votes
1answer
266 views
Expected value birthday problem compared to simulation
I'm having some trouble with the following modified version of the birthday problem: Calculate the expected value for the number of people questioned until the first match in the birthday problem, ...
1
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1answer
90 views
Random Variable Probability
Random variable X takes on the values 5, 20, 3, 200
they each take on the probabilities .60, .30, .08, .02 respectively. Use the statistical capacity of your calculator to find the expected
value of ...
1
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2answers
161 views
A Simple probability question
Suppose you are correct 90% of the time.
But in a particular case of 30 questions, you only get 15 correct. What are the odds of that?
2
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1answer
44 views
Functions of a Markov Chains
can does anybody know if the following expectations are available in closed for...
Let $\{ X_t : t = 1, 2, 3 \dots \}$ be a random variable defined on a Markov chain with m -step transition matrix ...
1
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1answer
67 views
trump cards question from Bayesian stats book
I'm looking at this problem in a bayesian stats book:
A card game is played with 52 cards divided equally between 4 players, North, South, East and West, all arrangements equally likely. 13 of the ...
2
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0answers
97 views
conditional expectation and order statistic
Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space.Let $\ X=(X_1,..,X_n)$ a random vector, with$\ n$ independents random variables whose law is $\mu$ on $\mathbb{R}$.
We define ...
5
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2answers
59 views
If n people enter a hall through any one of n doors, what is the probability at least one door is not used?
The probem is I have 2 conflicting solutions.
Solution 1:
Since there is $n$ people who each choose any one of $n$ doors, the total number of ways $n$ people enter the hall is $n^n$. (correct?)
...
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votes
1answer
44 views
cumulative probability
If the total no of trials is 4 and success ratio is 3:1 distributed in two classes.find the binomial probability obtained is 0.125.
similarly if total no. of trials is 33 and success ratio is 14:19 ...
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1answer
539 views
Example of non-mutually exclusive event using a coin
What I seen so far,
The probability of tossing heads is 1/2.
The probability of tossing tails is 1/2.
Therefore, the probability of tossing a coin for either tails or heads is 1 which is a mutually ...
1
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1answer
77 views
Probability of tossing a coin
This question comes from an exercise in book:
If I'm tossing coins. I tossed 2 heads in a row using a coin. What’s the probability now that the next coin will be heads?
Here's what I thought:
...
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1answer
46 views
By convention $P[X=x] = 0$ for all x. How would you explain pdf $f(x) =3x^2$ (where x is between 0 and 1) when x =0.9
By convention$ P[X=x] = 0$ for all x. How would you explain probability density function $f(x) = 3x^2$ (where x is between 0 and 1), probability is 0 otherwise. Then when x =0.9. f(x) > 1 which does ...
1
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1answer
62 views
Testing probability through an equation?
If a positive integer $n$ is picked at random from the positive integers less than or equal to $10$, what is the probability that $5n+3\le14$?
(A) $\displaystyle\large 0$
(B) ...
1
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1answer
90 views
Relation between a random variable and its conditional expectation
I have a random variable $X$ and its conditional expectation $E(X | G) = Y$.
In the context of some homework, I have to reach the conclusion that $P(X = 0 \text{ and } Y \neq 0) = 0$
But isn't this ...
1
vote
3answers
63 views
What is the probability of a product being defective, given subsequent observations?
Let's say I have a factory producing 28% defective bottles. A defective bottle has a 66.5% chance of breaking when dropped on the ground and a non-defective bottle only has a 9.5% chance to break.
...
2
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1answer
74 views
Probability of finding a fit for bin packing
Given that I know the total available space for a set of bins, and the number of bins, I'm trying to determine how likely it is that an item of size $n$ will fit into one of the bins.
As an example, ...
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1answer
36 views
Berry Esseen equation when skewness is zero
The Berry-Esseen theorem is a quantitative version of the central limit theorem which sets an upper bound on deviation from normality based on the sample size $n$. The equation for identically ...
1
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2answers
176 views
What does the value of a probability density function (PDF) at some x indicate?
I understand that the probability mass function of a discrete random-variable X is $y=g(x)$. This means $P(X=x_0) = g(x_0)$.
Now, a probability density function of of a continuous random variable X ...
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1answer
94 views
Making a uniform histogram by random numbers
I have a histogram which shows the frequency of elements in a set. I'd like to add minimum number of elements to the set such that the histogram of the set as defined above becomes fairly uniform. Is ...
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0answers
26 views
The asymmetric simple exclusion process understanding
Im currently looking into The asymmetric simple exclusion process. I am stuggling to understand the density and current within the model. From what I have researched the current depends on the ...
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2answers
156 views
Binomial distribution sample vs. population mean
I'm a little confused at this question posed by my prof. He asked us to generate a binomial distribution in R and input whatever variables we wanted.
...
1
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1answer
120 views
Showing that two variables do no have a bivariate normal distribution
If $X_1$ is $N(0,1)$ and $X_2 = -X_1$ if $-1 \leq X_1 \leq 1$ or $X_2 = X_1$ otherwise, how do you prove that $X_1$ and $X_2$ do not have a bivariate normal distribution?
Attempt: Using the Jacobian ...
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2answers
431 views
Interpreting Coin Toss Data. Biased or Not?
We have run an experiment in which some good chap has sat down and flipped a coin 100 times. At the end of the 100 flips he has tallied 40 Heads and 60 Tails. Now this seems like something is up with ...
1
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1answer
53 views
Counting Probabilities
An appliance comes in two colors, white and brown, which are in equal demand. A certain dealer in these appliances has three of each color in stock, although this is not known to the customers. ...
1
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1answer
78 views
Calculating probability from Poisson random variable
The number of times an individual contracts a cold in a given year is a Poisson random variable with parameter $\lambda = 2$. Suppose that a new wonder drug has just been marketed that reduces the ...
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2answers
46 views
Independence of 2 variables derived from dice rolls
A while ago, I was told that if you roll a d%,
by rolling 2 ten sided dice and treating one as the tens digit and the other as the ones,
then you can gain 2 independently distributed values by ...
1
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3answers
59 views
Confidence Interval Probabilty
1) We have discovered a new method to produce a liquid containing
Zinc. We measure the concentration μ four times independently (from
the same solution) and find the values
0.3, 0.33, 0.3, ...
1
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1answer
70 views
What is this question on random variables asking?
The question states:
A random variable $X$ is called symmetric about 0 if for all $x \in \mathbb R$, $\mathbb P(X \geq x) = \mathbb P(X \leq -x)$.
Prove that if $X$ is symmetric about 0, ...
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1answer
181 views
What does this distribution mean?
I'm kind of embarrassed that I don't fully get this, but I assume it is because the example is using letters for a sample space instead of numbers.
...
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3answers
62 views
What is the probability of a second queen being drawn?
A standard 52 card deck is used. It is randomly divided into two parts of 26 cards each. A card is selected from the first set, and it is found to be the Queen of Hearts. The Queen of Hearts is then ...
2
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1answer
94 views
Nash equilibria in games with infinitely many strategies
As a simple example, suppose two players A and B play a game wherein each picks a positive integer, and if they both pick the same integer $N$ then B pays $f(N)$ dollars to A, for some given payoff ...
2
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3answers
169 views
How can gender and class classification be dependent? [closed]
I got this question in my hw practice set
In a class, there are 4 freshman boys, 6 freshman
girls, and 6 sophomore boys. How many sophomore
girls must be present if sex and class are to
be ...
3
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3answers
81 views
True Randomness and repetition
I do not have a degree in any field of mathematics; however I would like to get an input perhaps from those who do.
I argued a point with one of my children the other day that if all of the arguments ...
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1answer
124 views
How do you prove that no matter whether P(A)=1 or 0, A is independent from B
Of course we are assuming that A and B are independent events. I know how to show that if P(A)=1 then P(B)=P(AB), but how do we show that if P(A)=0?
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2answers
90 views
Probability of an unprepared student passes a quiz, 3 of 7 must be correct with 4 possible answers each?
A quiz consists of 7 multiple choice questions, each with 4 possible answers. To pass the quiz, it is you must get at least 3 questions correct. An unprepared student can do nothing except guess ...
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1answer
88 views
Let $P(X=1)=0.6$ and $P(X=1,Y>=5)=0.2$. Find $P(X=1,Y<5)$.
I'm thinking with the given information $P(Y\geq5) = P(X=1,Y\geq5)/P(X=1)$, so $P(Y\geq5)=0.33$. Therefore, $P(Y<5) = 1-P(Y\geq5)$, so $P(Y<5)=0.67$. Which means $P(X=1,Y<5) = P(Y<5)P(X=1) ...
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2answers
125 views
How to calculate probably number of tries to guess someone's birthday in a room with N people?
A and B are sequences of random numbers where each number is an independantly random number from 1 to 365.
i and j are sequence positions in a and b
What's the probability that the set A(1..i) ...
1
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1answer
146 views
Let P(X=3)=0.4 and P(Y=2)=0.5. Find P(X=3,Y=2).
Let $P(X=3)=0.4$ and $P(Y=2)=0.5$. I need to find $P(X=3,Y=2)$.
I'm thinking that I ought to just multiply the two probabilities: $P(X=3) \times P(Y=2)$ to get $0.4 \times 0.5 = 0.2$, but is this ...
1
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1answer
124 views
A question about the expected number of games being played
refer to this question I wanna change the question, if the rule of the game is the same, what is the expected number played to end the game?
3
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1answer
342 views
Do hashing functions have a probability distribution calculated for their output?
This question might look strange, so I will try to be clear.
Consider a hashing function $f : M \mapsto H$ which takes a message with arbitrary length $m \in M$ as input and returns a hash $h \in H$ ...
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1answer
88 views
3 coloring of vertices in a graph
How can we prove that there exists a coloring of vertices for graph $G$ such that at least 2/9 fraction of all triangles in $G$ whose vertices have different colors?
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2answers
42 views
What is the chance that exactly 8 people have the same partners the second time?
25 people randomly form partners with each other. They sunder and do it again. What's the probability that exactly 8 people get the same partner the second time?
There are $\frac{25 \times 24}{2} = ...
5
votes
1answer
90 views
Generalization of Hoeffding Inequality
According to Hoeffding Inequality, if $X_1,\ldots,X_n$ are independent random variables with $\mathbb{P}(X_i \in [a_i,b_i]) = 1 \; \forall i = 1,\ldots,n$ then
$$\mathbb{P}(\bar{X_n} - ...
1
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1answer
51 views
What is the probability that no one has the same seat number for both concerts?
50 people each purchase a ticket for concert A and a ticket for concert B. The concerts both occur in an auditorium of 50 seats. If the seat numbers for the tickets are distributed randomly, what's ...
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2answers
89 views
What is this conditional probability asking?
I really dont understand how this info helps me solve this problem: In a study it was discovered that 25% of the paintings of a certain gallery are not original. A collector in 15% of the cases makes ...
