Theoretical Distributions

Theoretical Distributions

    Theoretical distributions are
      Theoretical Distributions
    Discrete Probability distribution
    Bernoulli distribution
    • A random variable x takes two values 0 and 1, with probabilities q and p ie., p(x=1) = p and p(x=0)=q, q-1-p is called a Bernoulli variate and is said to be Bernoulli distribution where p and q are probability of success and failure. It was given by Swiss mathematician James Bernoulli (1654-1705)

    Example

    • Tossing a coin(head or tail)
    • Germination of seed(germinate or not)
    Binomial distribution
    • Binomial distribution was discovered by James Bernoulli(1654-1705). Let a random experiment be performed repeatedly and the occurrence of an event in a trial be called as success and its non-occurrence is failure. Consider a set of n independent trails( n being finite), in which the probability p of success in any trail is constant for each trial. Then q=1-p is the probability of failure in any trail.
    • The probability of x success and consequently n-x failures in n independent trails. But x successes in n trails can occur in ncx ways. Probability for each of these ways is pxqn-x.
    P(sss…ff…fsf…f)=p(s)p(s)….p(f)p(f)….
    =p,p…q,q…
    =(p,p…p)(q,q…q)
    (x times) (n-x times)
    Hence the probability of x success in n trials is given by
    ncx pxqn-x

    Definition

    • A random variable x is said to follow binomial distribution if it assumes non-negative values and its probability mass function is given by
    Definition
The two independent constants n and p in the distribution are known as the parameters of the distribution.

Last modified: Monday, 19 March 2012, 7:22 PM