Study notes on Probability Distribution Functions for Mechanical Engineering

By Akhil Gupta|Updated : November 17th, 2020

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1. PROBABILITY DISTRIBUTION

1.1 Random Variables –

Suppose that to each point of a sample space we assign a number. We then have a function defined on the sample space. This function is called a random variable or more precisely a random function.

It is usually denoted by a capital letter such as X or Y. Random variable X associated with the outcome of an experiment which is not certain, and its value depend upon the chance.

If a random variable takes a finite set of values then it is called as Discrete random variable, whereas when a random variable takes an infinite set of values (or any value from a continuous range or graph) then it is called as Continuous Random variable.

1.2. Binomial Distribution –

Suppose that we have an experiment such as tossing a coin or rolling a die repeatedly or choosing a marble from an urn repeatedly. Each toss or selection is called a trial. In any single trial there will be a probability associated with a particular event such as head on the coin, 4 on the die, or selection of a particular colour of marble.

1.3. Poission’s Distribution –

1.4. Geometric distribution –

Consider repeated trial of Bernoulli experiment with probability of success p, and failure q=(1-p). if the experiment is repeated until success is not achieved, then the distribution of variable is given by geometric distribution.

If experiment is performed “k” times, then experiment must be failed in ‘K-1’ times.