Originally stated by the Reverend Thomas Bayes, this Bayes’ Theorem falls under probability theory and according to it, if E1, E2, E2, ……….,En are mutually exclusive and exhaustive events and A is any event then Proof :- Since E1, E2, E2, ……….,En are pairwise exclusive and …
A distribution which gives the probabilities of the values of a random variable function is called random variable distribution. If x1, x2,….,xn are random values of X and P1, P2,….,Pn are their corresponding probabilities, then the random variable distribution of X can be written as follow: …
Fuzzy Propositions :- Fuzzy propositions are assigned to fuzzy sets. Suppose a fuzzy proposition ‘P’ is assigned to a fuzzy set ‘A’, then the truth value of the proposition is proposed by T (P) = μA(x) where 0 ≤ μA(x) ≤ 1 Therefore truthness of a …
Given ‘X’ to be universe of discourse, A and B are two fuzzy sets with membership function μA(x) and μB(x) then, Union The union of two fuzzy sets A and B is a new fuzzy set A ∪ B also on ‘X’ with membership function defined …
Independent Events Two events A, B are said to be independent if and only if the Probability of (A intersection B) equals Probability of A multiplied to Probability of B. P(A∩B) = P(A). P(B) Note that, if A,B are independent events then P(B/A) = P(B) and …