probability mass function and probability density function

Although the probability distribution of a continuous r.v cannot be presented in tabular forms, we can have a formula in the form of a function represented by f(x) usually called the probability density function..

Let X be continuous random variable which can assume values in the interval [a,b]. A function f(x) on [a,b] is called the probability density function if ..

P{X = x} is called probability mass function..

1. If x is a discrete random variable assuming the values x 1 , x 2 , x 3 ,.,x n with probabilities p 1 , p 2 , p 3 ,., p n respectively then (x 1 ,p 1 ), (x 2 , p 2 ),(x n , p n ) defines a probability distribution of X. 2. Let n independent bernoulli trials be pe..

Binomial Distribution - A trial, which has only two outcomes i.e., "a success" or "a failure", is called a Bernoulli trial. Let X be the number of successes in a Bernoulli trial, then X can take 0 or 1 and P(X =1) = p = "probability of a success" P(X = 0) = 1 - p = q = "probability..

The Objective Function is a linear function of variables which is to be optimised i.e., maximised or minimised. e.g., profit function, cost function etc. The objective function may be expressed as a linear expressio..

Conclusion - In this chapter we have studied the method of evaluating probabilities of events relating to independent events and conditional events. We have also studied about random variables and their probability distributions, namely binomial distribution and Poisson distribu..

Random Variable and Probability Distribution - If is often very important to allocate a numerical value to an outcome of a random experiment. For example consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome : HH HT TH TT No. of heads (x) : 2 1 ..

If is often very important to allocate a numerical value to an outcome of a random experiment. For example consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome : HH HT TH TT No. of heads (x) : 2 1 1 0 x is called a random variable, which can assume the v..

Axiomatic approach to probability closely relates the theory of probability to set theory. Let S be the sample space of an experiment. Probability is a function, which associates a non-negative real number to every event A of the sample space denoted by P(A)..