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).

learn more… | top users | synonyms

2
votes
3answers
94 views

Conditional Probability with Normal Distributions?

Let's say that I have $3$ independent random normal variables, $A$, $B$ and $C$. They all have a standard deviation of $17.526$, while $A$ has a mean of $143$, $B$ of $139$, and $C$ of $129$. My ...
4
votes
2answers
63 views

Probability of two aces given at least one ace (out of two cards) vs probability of two aces given one card is the ace of spades (out of two cards)

So, in the video lectures from Harvard's Statistics 110:Probability course that can be found on iTunes and Youtube, I encountered this problem. https://www.youtube.com/watch?v=JzDvVgNDxo8#t=566 I ...
2
votes
2answers
79 views

Conditional expectation of $X$ given $Z = X + Y$

Suppose I have two independent normal variables $X$ and $Y$ with known mean and variance. Defining $Z = X+Y$, what is the most straightforward way to compute $\mathbb{E}\left[X|Z\right]$? I am ...
0
votes
1answer
20 views

Modelling a probability distribution on different feature sets

I have a binary classification problem, and I use method A and method B to extract features, F1 and F2, for this problem from dataset X. Now, I train two models, y1 and y2, separately on the two ...
0
votes
1answer
58 views

about the definition of bayesian network

In this PDF http://people.csail.mit.edu/yks/documents/classes/mlbook/pdf/chapter2.pdf page 5 says: Given a set of functions $f(x_i,pa(x_i))$ non-negative and sum to 1, we define a joint probability ...
0
votes
0answers
32 views

how to calculate Root Mean Square Error (RMSE) for predicted Probability Density Function (PDF) in Matlab

I have used Mixture Density Networks for probability density function prediction. I am wondering how I can calculate Root Mean Square Error (RMSE) of predicted pdf in MATLAB. Thanks.
1
vote
1answer
126 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, ...
3
votes
3answers
77 views

Binomial random variable conditional on another one

On the Wikipedia page for the Binomial distribution, the following property is mentioned (under the related distribution section): (paraphrased) If $X\sim \text{Bin}(n,p)$ and $Y|X \sim ...
0
votes
1answer
37 views

simply demostration on conditioned probability

I don't find the answer of this simply problem: how can I algebrically demonstrate that, with 3 variable A,B,C $ \sum\limits_C P(B|C)P(C|A)=P(B|A)$ under condition that $P(A,B,C)=P(A|C)P(B|C)P(C)$ ...
0
votes
0answers
16 views

Probabilities in a Markov Model

I am reading a paper on Markov Models and I am trying to figure out how to compute the probabilities for the $\alpha$-pass. I am given an $N\times N$ matrix $A$, that has the probabilities of ...
1
vote
1answer
22 views

What is full conditional distribution in my case?

If $\text{P}(M|D)$ is posterior, $a$ is the proportionality constant, $\text{P}(M)$ is the prior and $\text{P}(D|M)$ is the likelihood. I have the the prior distribution, and I know the function that ...
1
vote
0answers
19 views

What is the correct definition for completness in d-separation in directed graphical models?

I was reading Koller's book of probabilistic graphical models and in section 3.3.2 she discusses what properties should hold for d-separation as a method for determining independence. She tries to ...
2
votes
1answer
46 views

Maximum expected difference between players when using 4d6 drop lowest

Players of a certain TRPG have characters with 6 ability scores, each ability score ranging from 3-18. One method of generating those is by rolling 4d6 drop lowest for each of the scores. That means ...
2
votes
1answer
66 views

Probability for completely unfair stats when rolling ability scores using 4d6 drop lowest for D&D

Players of a certain TRPG have characters with 6 ability scores, each ability score ranging from 3-18. One method of generating those is by rolling 4d6 drop lowest. That means four six-faced-dice are ...
2
votes
2answers
116 views

What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?

I was reading Koller's and Friedman's Probabilistic Graphical Models book and became confused about some of its notation because of a set of notes that either contradict it or express it differently. ...
3
votes
2answers
43 views

Negating conditional probability

I'm refreshing on bayes theorem and conditional probability and I ran across these practice problems. I was trucking along until problem 9, which states: ...
3
votes
2answers
65 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 ...
2
votes
1answer
20 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
votes
1answer
69 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 ...
1
vote
0answers
22 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 ...
1
vote
1answer
27 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
votes
1answer
51 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 ...
1
vote
0answers
18 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 ...
1
vote
0answers
26 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 # ...
2
votes
0answers
48 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 ...
1
vote
0answers
14 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
votes
1answer
36 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 ...
1
vote
2answers
39 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 ...
1
vote
0answers
79 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 ...
0
votes
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
116 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
19 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
48 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 ...
0
votes
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 ...
1
vote
2answers
235 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
35 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 ...
0
votes
0answers
16 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 ...
1
vote
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 $n_s$ ...
0
votes
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)} $
0
votes
0answers
16 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
votes
0answers
34 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
32 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
votes
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
56 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
votes
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
56 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
93 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 ...
0
votes
0answers
21 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
529 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
votes
0answers
53 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 ...