{"id":16550,"date":"2019-12-30T19:09:15","date_gmt":"2019-12-31T00:09:15","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/?p=16550"},"modified":"2020-02-08T09:42:45","modified_gmt":"2020-02-08T14:42:45","slug":"part-3-some-basic-math-stat-concepts-for-the-wanna-be-data-scientists","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16550","title":{"rendered":"Part 3: Some Basic Math\/Stat Concepts for the wanna be Data Scientists"},"content":{"rendered":"

Conditional Probability and PDF<\/strong><\/p>\n

“The conditional probability<\/em><\/strong> of an event B<\/em> is the probability that the event will occur given the knowledge that an event A<\/em> has already occurred.<\/p>\n

This probability is written P(B|A)<\/em>, notation for the probability of B given A<\/em>. “<\/p>\n

\"\"<\/a><\/p>\n

“In the case where events A<\/em> and B<\/em> are independent<\/em> (where event A<\/em> has no effect on the probability of event B<\/em>), the conditional probability of event B<\/em> given event A<\/em> is simply the probability of event B<\/em>, that is P(B)<\/em>.<\/p>\n

If events A<\/em> and B<\/em> are not independent, then the probability of the intersection of A and B<\/strong><\/em> (the probability that both events occur) is defined by
<\/strong><\/p>\n

P(A and B) = P(A)P(B|A).<\/em><\/strong>” Multiplication rule<\/p>\n

Ref: http:\/\/www.stat.yale.edu\/Courses\/1997-98\/101\/condprob.htm<\/a><\/p>\n

Truncated Distribution<\/strong>
“<\/strong>In statistics<\/a>, a truncated distribution<\/strong> is a conditional distribution<\/a> that results from restricting the domain of some other probability distribution<\/a>. Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range.<\/p>\n

For example, if the dates of birth of children in a school are examined, these would typically be subject to truncation relative to those of all children in the area given that the school accepts only children in a given age range on a specific date. There would be no information about how many children in the locality had dates of birth before or after the school’s cutoff dates if only a direct approach to the school were used to obtain information.“<\/strong><\/p>\n

\"\"<\/a><\/p>\n

“<\/p>\n\n\n\n\n\n\n\n\n
Probability density function for the truncated normal distribution for different sets of parameters. In all cases, a<\/em> = \u221210 and b<\/em> = 10. For the black: \u03bc<\/em> = \u22128, \u03c3<\/em> = 2; blue: \u03bc<\/em> = 0, \u03c3<\/em> = 2; red: \u03bc<\/em> = 9, \u03c3<\/em> = 10; orange: \u03bc<\/em> = 0, \u03c3<\/em> = 10.<\/td>\n<\/tr>\n
Support<\/a><\/th>\n\"x<\/td>\n<\/tr>\n
PDF<\/a><\/th>\n\"\\frac{g(x)}{F(b)-F(a)}\"<\/td>\n<\/tr>\n
CDF<\/a><\/th>\n\"{\\displaystyle<\/td>\n<\/tr>\n
Mean<\/a><\/th>\n\"\\frac{\\int_a^b<\/td>\n<\/tr>\n
Median<\/a><\/th>\n\"{\\displaystyle<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

“<\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Truncated_distribution<\/a><\/p>\n

Law of Total Probability<\/strong>
\"\"<\/a><\/p>\n

Bayes\u2019s theorem<\/strong><\/p>\n

In probability theory and statistics, Bayes\u2019s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. Wikipedia<\/a><\/p>\n

Formula
\"P(A\\mid<\/p>\n\n\n\n\n\n\n
\"A,<\/td>\n=<\/td>\nevents<\/td>\n<\/tr>\n
\"P(A|B)\"<\/td>\n=<\/td>\nprobability of A given B is true<\/td>\n<\/tr>\n
\"P(B|A)\"<\/td>\n=<\/td>\nprobability of B given A is true<\/td>\n<\/tr>\n
\"P(A),<\/td>\n=<\/td>\nthe independent probabilities of A and B<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Ref: https:\/\/en.wikipedia.org\/wiki\/Bayes’_theorem<\/a><\/p>\n

Bayes Formula for Random Variables:<\/p>\n

http:\/\/pwp.gatech.edu\/ece-jrom\/wp-content\/uploads\/sites\/436\/2017\/08\/16_BayesRVs-su14.pdf<\/a><\/p>\n\n\t\t