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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2answers
36 views

If $X \sim$ unif$(0,1)$, what is the distribution of $U=\max \{X,1-X \}$?

Let $X$ be uniformly distributed in $(0,1)$ and set $U=\max \{X, 1-X\}$. How can I find the distributiopn of $U$? My first thought was to consider this a mixture distribution problem and use the CDF ...
1
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0answers
7 views

Estimating workers within Industry Sector using commuter data (combining probabilities?)

I have some detailed data about the commuting patterns of workers. If I know the following 3 things... The total number of workers commuting from one block to another. The total # and % of ...
4
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1answer
48 views

Verifying independence for two Random Variables

Could you please give me some hints for the exercise below? Suppose we toss a coin once and let $p$ be the probability of heads. Let $X$ denote the number of heads and let $Y$ denote the number of ...
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0answers
21 views

Non specific order of probabilities in a time step

I'm simulating a random collision process. At each time interval I calculate the probability of a collision occurring between each object and all other objects in proximity. Currently if I wish to ...
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1answer
22 views

Greater than 1 Naive Bayes Probabilities?

I am trying to train a Naive Bayes classifier. In addition to getting the most likely class as an output from the Naive Bayes classifier, I would also like to compute the probabilities associated with ...
2
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1answer
47 views

Bounded expectation implied bounded conditional or vice versa?

If $\mathrm{E}\left(X\right)<\infty$ does that imply $\mathrm{E}\left(X|Y\right)<\infty$? How about vice versa? I'm thinking if we condition on an event (say $Y>2$) then if we have ...
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0answers
14 views

How to find conditional distribution for Rao-Blackwellizing an estimator?

Let's say I have an unbiased estimator $u(\underline x)$ for function $v(\theta)$ where $\theta$ is a parameter of the distribution of $x$, and $T(\underline x)$ which is a sufficient statistic for ...
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0answers
24 views

Creating statistically balanced teams

Suppose that you have a tournament for a game with four players on each team. We also have a table that tells us overall statistics for each player. This table includes things like each player's # ...
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0answers
37 views

Some doubt in reading Machine Learning A Probabilistic Perspective ( chapter 3.2 )

When I am reading Murphy's Machine Learning A Probabilistic Perspective. In chapter 3.2. I have some doubt. I think the author want to express is two things. First, we can use Bayes formula to ...
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0answers
13 views

How to compute the marginal probability form conditional probabilities in logspace?

Normally the marginal probablity is computed as $p(x) = \sum_y p(x | y) \cdot p(y) $ Now, suppose I have all these probabilities at the right-hand side in logspace (so as logprobabilities). How do ...
2
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1answer
34 views

How to combine distributions

If I have two continuous distributions $f(x)$ and $g(x)$, there are several mathematical ways to combine $f$ and $g$ to get new distributions. Which correspond to what statistical interpretation? For ...
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2answers
38 views

Mixed variable, joint distribution, How do we know which one is continuous distribution, which one is discrete

If we have one continuous r.v. $x$ and a discrete r.v. $y$ which takes one of the two values $y_1$ and $y_2$. Let's say we know the prior probabilities $P(y_1)$ and $P(y_2)$. From Bayes theorem we ...
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0answers
78 views

Given $N$ samples from $p(x|y=y_0)$ how can I infer $y_0$?

I have $N$ samples $x_i \sim p(x|y)$ for $y = y_0$. I don't know apriori what $y_0$ is but I know its a fixed value. I do not have the analytic form of $p(x|y)$, $p(y|x)$, $p(x,y)$. Instead I have ...
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0answers
10 views

conditional probability, chemical reactor residence times

The following scenario is given in Dekking's "A Modern Introduction to Probability and Statistics" to illustrate conditional probability: "Consider a continuously stirred reactor vessel where a ...
4
votes
2answers
109 views

Does the formula $X|(Y,Z) =(X|Y)|(Z|Y)$ hold?

Suppose we have three absolutely continuous random vectors $X, Y, Z$. Can anyone prove the following formula? $$X|(Y,Z) =(X|Y)|(Z|Y)$$ Put differently $p(X|Y,Z)=p(\hat{X}|\hat{Z})$, where ...
2
votes
0answers
14 views

Estimating the non- parametric conditional probability

I have a set of observation from two parameters, let say $x$ and $y$ and then I want to make the conditional probability of $x$ for the given $y$, $p(x|y)$. So first I use ...
1
vote
1answer
47 views

Law of total probability on conditional

I often saw a formula, used mostly to integrate on the parameter space like: $$ p(x|y) = \int p(x|\theta) p(\theta|y) d\theta $$ where $\theta$ is the parameter. I am confused and I hope to explain ...
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0answers
13 views

Conditional Probability With Naive Bayes

I have recently begun exploring R I have downloaded a data set that contains flight times for when a plane takes off at Origin and Lands at destination The data has up to three months’ worth of ...
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2answers
234 views

Probability of x between two random variables

Given are $Z_1, Z_2$ i.i.d. standard normal. Find $P[Z_1 < t < Z_2]$ I have difficulties with working out how I should split the condition. Is $P[Z_1 < t < Z_2] = P[Z_1 < t, t < ...
2
votes
2answers
32 views

Crosscorrelation of stochastic process

Let $Z_1,Z_2 $ i.i.d. standard normal $$ X(t) = \begin{cases} 0, & \text{if } t<Z_1, t<Z_2\\ 1, & \text{if } Z_1\le t <Z_2 \text{ or } Z_2\le t <Z_1 \\ 2, & \text{if } t\ge ...
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0answers
13 views

Measuring NN saturation: calculating probabilities

I am trying to devise a measurement of neural network saturation for my NN saturation study. Some background: saturation occurs when a hidden neuron outputs values close to the extremes (usually 0 and ...
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0answers
15 views

Clarification of an equality involving conditioning

In this wikipedia section, the first block equation claims that $P(n_b \leq n^* | s+b)=P(n\leq n^* | b)$ Some context (also found in that linked section): $n_b$ follows $Pois(b)$ and $n_s$ ...
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0answers
22 views

Conditional distribution in a Bayes net

I have this Bayesian network where variable C is dependent on variables A and B. I want to know how come $ P(B|C) = \frac{P(B)}{P(B)+(1-P(B))P(A)} $
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0answers
10 views

Transition matrix in left-right hidden semi-Markov model

i'm developing a hidden semi-Markov model left-right . In a left-right model a sequence of $M$ states starts in state 1 and ends in state M, with no repetition of states. Since the model is ...
2
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0answers
27 views

Sample data from combination of two probability distributions

I want to generate a mock catalogue. I have access to two independent sets of real data and I want to use their properties to make the mock catalogue: The first one contains the information from ...
2
votes
2answers
26 views

Conditional distribution of uniform random variable distributed over (0,1)

Let $U$ be a random variable uniformly distributed over (0,1). Compute the conditional distribution of U given that $U>a$ The solution says: $P(U > s | U > t) = \frac{P(U > s)}{P(U > ...
2
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1answer
25 views

Question about the probability chain rule

I've understood from this: Is this a correct statement of the probability chain rule? that in the chain rule for probability, conditioning can be done on different variables. I was wondering what ...
2
votes
1answer
43 views

Can Someone Explain How Factor Multiplication Works with Factor Graphs?

I'm taking the Probablistic Graphical Model course here: https://class.coursera.org/pgm-003/ This class uses the concept of Factors extensively with regards to graphical models: ...
4
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0answers
65 views

What if P(A|B)=P(B|A)?

If we have P(A|B)=P(B|A), then what is this special case called and are there special properties? I'm interested in a simpler way of computing one of them and would like to take advantage of such ...
0
votes
0answers
45 views

Calculate conditional probabilities on a logistic regression

I am analysing data of an digital advertising tool. I have access to all the exposures for each of the 6 channels (x1, x2, .., x6) of an online campaign. The outcome is the conversion (y=1 or 0) on ...
2
votes
2answers
90 views

Drawing pair of cards. Did my brother play fair or unfair?

The Game There is a pool of $n$ cards that are marked either by a A or by a B. There is a proportion $p$ of the cards that are ...
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0answers
20 views

Conditional Independence over evidences

Suppose that we have different evidences $e_1, e_2, \ldots$, and we know the conditional probability of event $t$ over each of them, say $P(t|e_i)$. Now I have a set of observed evidences $e_i$, and ...
2
votes
3answers
446 views

Algorithm for winning casino roulette

I would like to try the following algorithm in order to win in the roulette: Be an observer until there are 3 same parity numbers in a row ($0$ has no defined parity in this context) Once there were ...
0
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0answers
50 views

Conditional probability and Bayes theorem

Precision Tool Company owns a five-year-old truck. After careful consideration, management has decided that there is a one in five chance that the truck will have to have major repairs within the next ...
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0answers
19 views

Conditional inverse Gaussian distribution

I am considering the Inverse Gaussian distribution as the hitting time distribution for a Wiener process, $W(t)$, with drift parameter $\nu$ and variance parameter $\sigma$. Define the hitting time as ...
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0answers
7 views

distribution of sample mean conditional on partially observed data

I want to find the sampling distribution of the mean of a sample of n Gaussian RVs with unknown $\mu, \sigma$ - conditional on the mean of the first k < n samples being known. Is there any chance ...
3
votes
4answers
374 views

Given more information, can a probability lessen?

Let $A$, $B$ and $C$ be events in the same probability space. Does $$\begin{align} \mathbb P(A\,|\,B\cup C) \ge \mathbb P(A\,|\,B) \end{align}$$ hold?
6
votes
1answer
118 views

Total expectation theorem for Poisson processes

I have two independent Poisson processes $A$ and $B$ with arrival rates $\lambda_A$ and $\lambda_B$, respectively. Now, the expected time for the arrival of the next item for the merged process should ...
0
votes
1answer
37 views

Bayes rule and conditional independence

I have two conditionally independent random variables $A$, $B$ such that $$ P(A,B\mid C) = P(A\mid C)P(B\mid C) . $$ I have to find posterior formula $P(C \mid A,B)$. My result with a ...
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0answers
23 views

How can I calculate Conditional Probability of the following case? [duplicate]

Recently I attended a workshop on probability, I was asked the following question but I did not find a way to solve it. A discussion on this question can help to learn something new. We were told ...
0
votes
1answer
47 views

Marginalisation on conditional probability

I'm afraid this is an extremely simple question, but I didn't understand completely why if both $O_1$ and $O_2$ can be marginalised over $R$ the following holds: $ P(O_2 = o_i | O_1 = o_j) = \sum_r ...
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0answers
34 views

A simple application of conditional probability

I am practicing using conditional probability and have the following question Suppose the probability of contracting a rare tropical disease Chickungunya on a holiday to India is 0.0001. Fred, on his ...
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0answers
32 views

Probability of winning given competitor pair analysis

Given an analysis of every pair of competitors in a race, how may I determine the probability of any given competitor winning the race? For example, what is the probability of competitor 2 winning ...
1
vote
1answer
67 views

Conditional density and variance of Nadaraya-Watson model

Given N data points x and N targets t, considering a new point x and the corresponding new target t What would be: The conditional density The conditional mean variance of the ...
0
votes
1answer
67 views

Proving conditional independence from mutual independence

Suppose I have a Bayesian inference problem where $E$ is the result of a chemistry experiment. The chemistry experiment consists of a controlled sequential digestion of one end of the protein using a ...
6
votes
2answers
322 views

A generalization of the Law of Iterated Expectations

I recently came across this identity: $$E \left[ E \left(y|x,z \right) |x \right] =E \left(y | x \right)$$ I am of course familiar with the simpler version of that rule, namely that $E \left[ E ...
2
votes
2answers
73 views

Self Study question on Conditional Probability

I am currently doing a self-study on Conditional Probability. I was faced with a question where I was provided with $P(a)$, $P(b)$, $P(c)$, $P(a \mid d)$, $P(b \mid d)$ and $P(c \mid d)$. The full ...
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0answers
24 views

Conditional independence proof seems too obvious, am I looking at it incorrectly?

I'm given the following question about conditional independence: "Suppose we have four random variables a, b, c, d. Prove that, if a is conditionally independent of b and c given d, then a is ...
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1answer
53 views

Problem with estimating probability using the multivariate Gaussian

I'm working on a problem where I need to find the probability of a given data sample belonging to a give class using the Bayes Theorem for classification. From everything I've been able to find so ...
0
votes
1answer
28 views

Is there any way to merge two conditional probability distributions?

Is there any way to construct an expected conditional probability distribution of the form p(x|(y,z)) if I am starting with p(x|y) and p(x|z)? All variables are categorical. My specific problem deals ...