Number of grand slam final matches won by a tennis player is a Binomial Random variable. Each time the player enters into the finals is a trial – with two outcomes – success or failure.In her or his career, the player would have played grand slam finals for 10 times.Then the number of trials is ‘n’, which is a parameter of Binomial Distribution.Each time the player participates in the final, the probability of winning the match is 50 – 50.
With Continuous Uniform Distribution same probabilities are assigned for a range of values. In other words the height of the distribution is constant for several range of values.
If the Logarithm of continuous Random Variable X is normally distributed, then the Random Variable X follows a normal distribution for positive values of X. Similarly if a continuous random variable Y follows normal distribution then X = exp(Y) follows log-normal distribution.
Gamma distribution is used to model the arrival times in Poisson Process. The long running average λ in the Poisson distribution follows Gamma distribution. Gamma distribution is a continuous distribution.
In case of a fair coin toss, the probability ‘p’ of getting a head is 0.5 and probability of getting a tail is 1-p which is 0.5. If the coin is a biased coin The p value will be greater than or smaller than 0.5 and so is the value of 1-p.
Poisson distribution is about modeling a rare event occurrence and is referred as Law of Improbable Events. Modeling the failure of Aircraft Engines over a period of time is an example of applying Poisson distribution.
Exponential distribution is a continuous distribution used for modeling the probabilities of time taken between two events of a Poisson process where the event rate is a positive constant denoted by λ.
Weibull Distribution is used in modeling reliability of components and materials.The distribution is named after the Swedish Engineer Ernst Hjalmar Waloddi Weibull.
A Continuous Random Variable X following Beta Distribution with parameters α,β is denoted as Beta (α,β). The distribution is defined for a continuous random variable taking values from 0 to 1.