# probability Archive

## Arithmetic Mean, Variance and Standard Deviation of a Random Variable Distribution

Suppose the random variable distribution of a random variable X is as follows: X = xi P(x = xi) x1 x2 x3 . . . xn P1 P2 P3 . . . Pn Then, Arithmetic Mean μ = Variance σ2 = Standard Deviation σ ...Read More

## Multiplication Theorem of Probability

According to Multiplication Theorem of Probability, for any two events A, B probability of A∩B is as given below P(A∩B) = P(A).P(B/A) = P(B).P(A/B) Suppose N is the total number of simple events in the sample space S. Simple events in A∩B = λ1, ...Read More

## What is Probability?

If S is the sample space of a random experiment, ‘E’ is any event, then probability of E is denoted by P(E) and is defined as P(E) = (Number of Simple Events in E / Total Number of Simple Events in S.) Note that, ...Read More

## Proof of Addition Theorem on Probability Through Axiomatic Approach

According to Addition Theorem on Probability, for any two elements A, B P(A∪B) = P(A) + P(B) – P(A∩B) Addition Theorem on Probability Proof :- Expressing A∪B as the union of two mutually exclusive events we get(A∪B) = A ∪ (B-A)P(A∪B) = P(A ∪ ...Read More

## Addition Theorem on Probability

For any two event A, B the Probability of A union B equals to probability of A added to probability of B minus probability of A intersection B. P (A∪B) = P(A) + P(B) – P(A∩B) Proof :- Suppose, the simple events in A∩B ...Read More