The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

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40 views

Distribution of $e$ if $g=\tilde{g}+e$, $g=|f|$, $f \sim \mathcal{N}(0,1)$ and $\tilde{g}$ is the quantization of $g$

Let $f \sim \mathcal{N}(0,1)$ be a normal random variable with zero mean and unit variance. Let $g=|f|$. Let $\tilde{g}$ be the quantization of $g$. We suppose that there are $n$ possible levels of ...
3
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2answers
46 views

Inequality of binomial probabilities

I need to show the following: I have two binomial random variables $X \sim BIN(m,p_1)$ and $Y \sim BIN(m,p_2)$, where $p_2 \geq p_1$. I want to show for any fixed constant $c \in \{0,...,m-1\}$ that ...
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0answers
15 views

What tests and plots to use with conditional probability?

I have datapoints collected from Italian students' curricula, including final marks received for one Exam (between 18 and 31) and their Final Degree (cum- or sine-laude). I’m interested in studying ...
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0answers
30 views

What is the Bernoulli class conditional distribution?

What is the Bernoulli class conditional distribution? I am trying to implement a procedure for computing a naive Bayes classifier for binary features with a Bernoulli class conditional distribution. ...
0
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1answer
30 views

How to find the probability that a group of people is not allowed to enter a country given some factors?

I have this scenario: There are two countries A and B. A sends a group of N people to B... There is an independent probability of p that a person gets fatigued while traveling to B. And I have ...
2
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0answers
11 views

Explanatory power of variable

To clarify from the very beginning, I expect relations between my variables to be very non-linear, so usual correlation and PCA approach may not work here. Also, for simplicity all the variables are ...
3
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0answers
38 views

Expectation of a conditional density

I'm trying to figure out why the following equation holds: $$f_{Y}(y) = E(f_{Y|X}(y|X))$$ I have sort of "worked out" the RHS to be: \begin{align} f_{Y}(y) &= E(f_{Y|X}(y|X)) \\[5pt] ...
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0answers
31 views

Proof of inequality [closed]

Can any one help me to prove this question: Let B ⊂ F be a sub σ-algebra inequality (|x||y|)/αβ ≤ x^2/(2α^2 )+y^2/(2β^2 ) with αβ>0 to prove E{|xy||B}≤αβ
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0answers
21 views

Find the CDF of a random variable given its relationship to a second random variable? [closed]

Take a lifetime with the CDF $F(t)=1-(1-t)^n$ for $t$ in $[0,1]$ and some natural $n$. Now find the CDF of the variable $T_x=T-x$ when $T>x$ for $x$ in $(0,1)$. I need help getting started on this ...
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1answer
24 views

How to calculate $P(A)$ given only $P(A|B)$ , $P(A|B')$ and $P(B)$?

Assume $A$ and $B$ are two dependant events with only the following details provided $P(A|B)$, $P(A|\neg B)$ and $P(B)$ How to calculate the value of $P(A)$?
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2answers
55 views

Finding the conditional distribution of 2 dependent normal random variables

Here's the situation $X \sim N(\mu, \sigma^2)$ and given $X=x$, $Y \sim N(x, \tau^2)$ I need to find the distribution of $X$ given $Y=y$ From what's given, I know the pdf's of $X$ as well as ...
0
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0answers
20 views

conditional probability symbol “;”? [duplicate]

Is it a conditional probability? Is ";" the same thing as "|"? if yes, why the writter use ; rather than |?
0
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2answers
52 views

Estimate point in metric variable where probability of success of a conditionally Bernoulli distributed variable changes (independent observations)

There is a metric variable X and a conditionally Bernoully distributed variable Y, where the probability of success of Y changes at a threshold x of variable X. The obervations are independent. I want ...
0
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1answer
31 views

Is $E[1_A | \mathscr{F_t}] = 0 ~\text{or} ~ 1 \ \Rightarrow E[1_A | \mathscr{F_{s}}] = E[1_A | \mathscr{F_t}]$ is only almost surely?

Spin-off from my previous question: Prove/Disprove $E[1_A | \mathscr{F_t}] = 0 ~\text{or} ~ 1 \ \Rightarrow E[1_A | \mathscr{F_{s}}] = E[1_A | \mathscr{F_t}]$ Apparently the conclusion holds true ...
2
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2answers
66 views

Why does a probability of 0 or 1 remain unchanged with new information, intuitively?

Related to these questions: Prove/Disprove $E[1_A | \mathscr{F_t}] = 0 ~\text{or} ~ 1 \ \Rightarrow E[1_A | \mathscr{F_{s}}] = E[1_A | \mathscr{F_t}]$ Does an unconditional probability of 1 or 0 ...
3
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2answers
34 views

Balls in Bins Problem

Let there be $n$ bins. Each $i^{th}$ bin contains $n-i$ white balls and $i-1$ black balls. If a bin is picked at random from which two balls are picked without replacement. What would be the ...
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1answer
23 views

Metrics to asses the ability of a model to predict a probability

Problem setting Here is the problem. A customer is faced to several products corresponding to the needs he has expressed. The goal is here to predict the probability of each product to be chosen. ...
1
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2answers
34 views

How to do I expand this conditional, joint probability?

Is $\Pr(y \ , \mu |, H_0)$ equal to $\Pr(y \ | \mu)\Pr(\mu | H_0)$ or $\Pr(y \ | \mu , H_0)\Pr(\mu | H_0)$?
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0answers
10 views

Characterization of point process, given the number of points

For a point process with independent and identically distributed inter-renewals, with distribution $p(x)$, we observed $N$ points on $[0,T]$. What is the probability distribution function of the ...
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1answer
34 views

sock drawer problems and sampling without replacement

Could I get help on this "sampling without replacement" question please? In a drawer, there are 10 socks, six RED and four BLUE. Q1: If you were to get four socks in a row, what is the probability ...
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2answers
51 views

Why doesn't P(x|y) determine P(x,y)?

This is a sort of paradox that has me confused. i just need some help clearing things up. Let $x,y$ be two discrete, finite variables, where $x$ can take on $N$ values and $y$ can take $M$ values. ...
2
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0answers
40 views

Combining multiple classifiers

I am trying to do a binary classification of text articles into {relevant, non-relevant}. The text articles have following features: [[article text, ...
0
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1answer
19 views

Probability that only one component is defective?

A component has a probability of 0.05 to have a certain defect (a) and 0.01 to have another defect (b). The two defects are independent. I have to find the probability that the component has only one ...
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0answers
36 views

Train & predict probabilities using LDA having multiple collinearities

I am trying to fit an LDA model and predict conditional probabilities of class membership with it. I believe I understand the basic method to do this using the covariance matrix and class means, but ...
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2answers
75 views

Probabilities of betting odds not adding up to 1

I am currently studying logistic regression. So the Probability(p(x)) of assigning an outcome is calculated as : $\frac{p}{1-p} = e^{\beta_0 +\beta_1X} $ Further, I read that the fraction on the ...
3
votes
1answer
28 views

Conditional Expectation of sum of uniform random variables?

Let $X,Y$ be independent uniform random variables on interval $[0,1]$. Can someone show me how to find the expectation of $X$ conditioned on $X+Y \ge (\text{say}) 1.3$? $$E[X | (X+Y) \ge 1.3]$$ ...
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0answers
16 views

Test for Conditional Normality?

On page 357 of this article, it states: We assume that the treatment (or its transformation) has a normal distribution conditional on the covariates. How would I go about determining if a ...
0
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0answers
15 views

How to work out complicated forms in probability? [duplicate]

Assume a population of $10^9$ people, tracked over a 1000 days. A person stays in a hotel for a probability of 1% in any given day. Each hotel hosts 100 people at a time. How many pairs of people ...
3
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0answers
30 views

Cox's Theorem: the necessity of (un)countably additivity

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
0
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0answers
12 views

Cox's Theorem: controversy surrounding the proposition domain size

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
1
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0answers
7 views

Cox's Theorem: ignorance, objective priors, and the Mind Projection Fallacy

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
3
votes
0answers
18 views

Cox's Theorem: controversy surrounding universal comparability

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
0
votes
0answers
18 views

A conditional normal random variable conditioned on a normal distributed random variable

I am trying to solve the following problem. Given $S \sim N(\mu_S,\sigma_S^2)$ and $U| S=s \sim N(s p,sp(1-p))$, what is the distribution of $U$? By the central limit theorem (CLT), the conditional ...
0
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1answer
15 views

Getting P(X) from Joint Probability Table P(X, Y) [closed]

I am trying to get the P(X) from this joint probability P(X,Y) table: X=1 X=2 X=3 Y=a 0.10 0.20 0.30 Y=b 0.05 0.15 0.20 I think the formula to find this ...
3
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0answers
32 views

The variety of problems with Cox's Theorem [closed]

So I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
5
votes
1answer
111 views

Sum of coefficients of multinomial distribution

I'm throwing a fair die. Whenever I get a 1, 2, or 3, I write down a '1'; whenever I get a 4 I write down a '2'; whenever I get a 5 or a 6, I write down a '3.' Let $N$ be the total number of throws I ...
0
votes
1answer
37 views

How to calculate prior probabilities

I have two possible events $A$ and $B$ that could lead to $n$ possible consequences $X_1, X_2, \ldots , X_n$, $P(A) + P(B) = 1$, $P(X_1) + P(X_2) + \ldots + P(X_n) = 1$. I know all conditional ...
1
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0answers
23 views

Can the probabilities of classification trees be compared with the ones from logistic regression?

When I use the same data set to estimate a tree and a logistic regression model. Is there a way of comparing the resulting probabilities? In my view, there is not. Because, for logistic regression, I ...
0
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0answers
29 views

With given numbers $a_1, a_2,a_3,…,a_N$, let $W=\Sigma_{i \in s_n}a_i$. Calculate the mean and variance of $W$

From the set $R=\{1,2,3,...,N \}$, a set $s_n$ of $n$ numbers are chosen without replacement, $0<n<N$. With given numbers $a_1, a_2,a_3,...,a_N$, let $W=\Sigma_{i \in s_n}a_i$. Calculate the ...
1
vote
1answer
47 views

Consistent estimator of the expectation of a conditional probability

I'm stuck in a problem where I have distribution distribution $P(\boldsymbol{x})$, from which I know how to sample from (i.i.d.) and two functions of the random variable $\boldsymbol{x}$: ...
1
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1answer
26 views

An algebra of the joint and conditional 'operators'

In treatments of Bayesian methods you typically see terms combining joint distributions with conditional distributions such as $P(A,B|C)$ and $P(A|B,C)$. Expressions arise such as the chain rule $$ ...
2
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0answers
48 views

For each x, I observe A and know P(C). What can I say about E(A|C)?

For each subject x in a population, I observe x's age, A(x). I can calculate the probability that x has some property of interest c, $P[C(x) = 1]$, where C(x) is a binary variable indicating ...
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0answers
41 views

How can we say that $B_n$ is a Markov process (or something)?

From Probability with Martingales: I chose $\mathscr F_n = \sigma(B_1, B_2, ..., B_n)$. My argument assumes that $E[M_n | \mathscr F_{n-1}] = E[M_n | B_{n-1}]$. I was able to show that ...
8
votes
1answer
314 views

Bayes Theorem with multiple conditions

I don't understand how this equation was derived. $P(I|M_{1}\cap M_{2}) \leq \frac{P(I)}{P(I')}\cdot \frac{P(M_{1}|I)P(M_{2}|I)}{P(M_{1}|I')P(M_{2}|I')}$ This equation was from the paper "Trial by ...
6
votes
2answers
140 views

Train waiting time in probability

Let's say a train arrives at a stop every 15 or 45 minutes with equal probability (1/2). What is the expected waiting time of a passenger for the next train if this passenger arrives at the stop at ...
0
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0answers
28 views

Probability that a query is wrong given results are correct

This question might be practically useless but I'm trying to work through a thought experiment here. Lets say I have a query that I run on a monthly basis and I want to know if the query is written ...
4
votes
0answers
27 views

Estimation of sample mean for hypergeometric distribution under a constraint

Assume that we have a dataset $D$ that contains the age of N people: $X_1, \dots , X_N$. We draw a sample $S$ of size $n$ using sampling without replacement ($Y_1, ... , Y_n$). In order to estimate ...
3
votes
1answer
85 views

How to interpret this notation with a tilde?

The following convention is sometimes encountered in the text (here example from HMM statement, $\{X_n\}_{n \geq 1}$ is a Markov process): $$X_n \mid (X_{n-1} = x_{n-1}) \sim f(x_n \mid x_{n-1})$$ ...
0
votes
2answers
24 views

Making inferences from Bayes networks and CPTs

So I'm practicing working with Bayes Networks and conditional probability tables and I feel like some of my numbers simply don't make sense. Here's the situation: I have a bag of three different ...
1
vote
1answer
22 views

How to compute the entropy of the specific conditional probability

Consider a random variable $X$ to be uniformly distributed in a domain $\Omega$, $$P(x) = 1/|\Omega|$$, with $|\Omega| = \int_\Omega dx$. Consider a second random variable defined by $Y=f(X)$, such ...