![]() x n) - is any function of n variables x 1, x 2. Determine whether a function belongs to each of the five Post's classesīoolean function f(x 1, x 2.Construct the Zhegalkin polynomial (by Pascal, triangle, and undefined coefficients methods).Construct a perfect disjunctive normal form (DNF).Construct a perfect conjunctive normal form (CNF). ![]() To change the order of operations round brackets are used (). Where both all logical operations and a set of the most commonly used variables are available. Operation symbol, then use the calculator keyboard (if it is not visible, press "Show Keyboard"), If your keyboard does not have the desired >, =), and symbols established in literature ( ∧, ∨, Specify whether the output of the solution is required by the "With solution (By the steps)" switchĪs variables, the letters of the Latin alphabet are used, as well as numbers written after the letter (variable index).īoth normal keyboard characters ( *, +, !, ^,.Specify the actions to be performed using the switches.Enter in the field logic function (for example, x1 ∨ x2) or its vector (for example, 10110101).Bayes' theorem is helpful in weather forecasting.It is used to calculate the next step of the robot when the already executed step is given.Putting all values in equation (i) we will get: Application of Bayes' theorem in Artificial intelligence:įollowing are some applications of Bayes' theorem: P(Face|King): probability of face card when we assume it is a king = 1 P(face): probability that a card is a face card= 3/13 P(king): probability that the card is King= 4/52= 1/13 The probability that the card is king is 4/52, then calculate posterior probability P(King|Face), which means the drawn face card is a king card. Question: From a standard deck of playing cards, a single card is drawn. Hence, we can assume that 1 patient out of 750 patients has meningitis disease with a stiff neck. Let a be the proposition that patient has stiff neck and b be the proposition that patient has meningitis. The Known probability that a patient has a stiff neck is 2%.The Known probability that a patient has meningitis disease is 1/30,000.He is also aware of some more facts, which are given as follows: Question: what is the probability that a patient has diseases meningitis with a stiff neck?Ī doctor is aware that disease meningitis causes a patient to have a stiff neck, and it occurs 80% of the time. Suppose we want to perceive the effect of some unknown cause, and want to compute that cause, then the Bayes' rule becomes: This is very useful in cases where we have a good probability of these three terms and want to determine the fourth one. Applying Bayes' rule:īayes' rule allows us to compute the single term P(B|A) in terms of P(A|B), P( B), and P(A). Where A 1, A 2, A 3., A n is a set of mutually exclusive and exhaustive events. In the equation (a), in general, we can write P (B) = P(A)*P(B|Ai), hence the Bayes' rule can be written as: P(B) is called marginal probability, pure probability of an evidence. P(A) is called the prior probability, probability of hypothesis before considering the evidence P(B|A) is called the likelihood, in which we consider that hypothesis is true, then we calculate the probability of evidence. P(A|B) is known as posterior, which we need to calculate, and it will be read as Probability of hypothesis A when we have occurred an evidence B. ![]() It shows the simple relationship between joint and conditional probabilities. This equation is basic of most modern AI systems for probabilistic inference. The above equation (a) is called as Bayes' rule or Bayes' theorem. Equating right hand side of both the equations, we will get:
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |