Wandering around

Given an object recognition system, I obtain the confident values of whether or not an object appears in an image. I want to find out whether or not an action is likely to happen given such objects' appearance probability. I can model such a system using conditional probability, e.g., the probability of action A given the appearance of object O1, and without the appearance of object O2, etc. Could Topic models or any LDA-style model help in this case?

We randomly distribute n points on the circumference of a circle. What is the probability that they will all fall in a common semi-circle? (read from here )

A random variable is a mapping from a sample space to real numbers $\Omega \rightarrow \mathrm{R}$ At a certain point in most probability courses, we don't see the sample space, but it's always there, lurking in the background. For example: Let $\Omega = \{(x,y); x^2 + y^2 \leq 1\}$ be the unit disc. Consider drawing a point "at random" from $\Omega$. Outcome: $\omega = (x,y)$. Examples of random variables: $X(\omega) = x$, $X(\omega) = y$, $Z(\omega) = x + y$

I divide my email into three categories: A1 = spam. A2 = low priority, A3 = high priority. I find that: P(A1) = .7 P(A2) = .2 P(A3) = .1 Let B be the event that an email contains the word "free". P(B|A1) = .9 P(B|A2) = .01 P(B|A3) = .01 I receive an email with the word "free". What is the probability that it is spam?

Every problem will get more complicated when coming to infinite

1. Counting theory: We may all remember: Given n objects, the number of ways of ordering these objects is: n! = n(n-1)(n-2)..3.2.1. n choose k, which is the number of distinct ways of choosing k objects from n: (n k) = n! / ( k! * (n-k)! ) For example: If we want to form a random group of 3 students among 20 students, there are: 20! / (3! * 17!) = 1140 possible groups 2. Probability - First problem: Discrete probability distribution for the sum of two dice. - Second problem: Two people take turns trying to sink a basketball into a net. Person 1 succeeds with probability 1/3, person 2 with 1/4. What is the probability that person 1 succeeds before person 2?

Following "A concise Course in Statistical Inference", I will start summarizing the main ideas. Data analysis, pattern recognition, machine learning, data mining are general terms that we have seen a lot, which indeed refer to special cases of statistical inference. Particular problems are classification, prediction, clustering, estimation. - In Probability, we study: Given a data generating process, what are the properties of the outcome? - In Statistical Inference, we study: Given the outcomes, what can we say about the process that generated the data? This first entry will devote for "Probability". Probability theory, or probability distribution/density is a function that describes the probability of a random variable taking certain value. There are two kinds: - Discrete probability distribution (or probability on finite sample spaces): characterized by a probability mass function uniform probability distribution: if the sample space is finite and each outcome is