Distribution Function of Exponential distribution, Memoryless Property of Exponential Distribution
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
Explain about the exponential distribution, distribution function of exponential distribution and memoryless property of exponential distribution
Rectangular Distribution
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
A random variable X is said to have a continuous uniform distribution over an interval (a, b) if its probability density function is a constant = k, over the entire range of X. (i.e.,) f(x) = K, a < x
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
Geometric distribution has a important application in queueing theory, related to the number of units which are being served or waiting to be served at any given time.
Poisson Distribution with Problems
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
The Poisson probability distribution was introduced by S.D. Poisson in a book he wrote regarding the application of probability theory to law suits, criminal trials, and the like.
Bernoulli Trial, Binomial Experiment, Additive Properties of Binomial Random Variable
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
An experiment consisting of a repeated number of Bernoulli trials is called Binomial experiment. A binomial experiment must possess the following properties. a. There must be a fixed number of trials. b. All trials must have identical probabilities of success (p) c. The trials must be independent of each other.
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
1. A random variable X may have no moment although its m.g.f exists. 2. A random variable X can have its moment generating function and some (or all) moments, yet the moment generating function does not generate the moments. 3. A random variable X can have all or some moments, but moment generating function do not exist except perhaps at one point.
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
A random variable X is said to be continuous if it takes all possible values between certain limits say from real number 'a' to real number 'b'. Example: The length of time during which a vacuum tube installed in a circuit functions is a continuous random variable. Note: If X is a continuous random variable for any x1 and x2 P(x1 ≤ X ≤ x2) = P(x1 < X ≤ x2) = P(x1 ≤ X < x2) = P(x1 < X < x2)
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
A random variable is a rule that assigns a numerical value to each possible outcome of an experiment.
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
Definition, explanation and problems of baye's theorem
Marginal probability, Joint probability, Conditional probability, Conditional probability of a sample point, Relationship between conditional, joint and marginal probabilities
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
The conditional probability of A given B is P (A/B) = P(A∩B)/P(B) if P(B) ≠ 0 and it is undefined otherwise.
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
Important problems under (i) P(AUB) = P(A) + P(B) - P(A∩B) (ii) P(A∩B) = P(A) . P(B)
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
Important Problems on P(AUB) = P(A) + P(B) (or) P(A + B) = P(A) + P(B)