Question

What is the difference between a discrete
probability distribution and a continuous
probability distribution?
Give your own example of each. What is the
expected value, and what does it measure?
How is it computed for a discrete probability
distribution?

Answer 1

solution:

Probability Distribution: A Probability Distribution is a formula (or) table used to assign probabilities to each possible values of a random variable . A Probability Distribution may be either Discrete (or) Continuous Distribution.

The following are the difference between Discrete probability Distribution and Continuous probability Distribution

Discrete Probability Distribution

Continuous probability Distribution

1. In Discrete probability Distribution the random variable can take finite number of Discrete values. 2.If a random variable is Discrete random Variable then it's probability Distribution is known as ' Discrete probability Distribution'. 3.Here, The probability Mass Function(PMF) is a probability distribution of discrete random variable which provides the possible values and associated probabilities.It is represented by P(X). 4.The probabilities associated with each possible values must be positive and sum upto 1.For all other values the probabilities need to be zero. 1) 2) P(X) > 0 5. The following distributions are some distributions that comes under discrete probability distributions ---> Binomial distribution ---> Poisson Distribution --->Hypergeometric Distribution ---> Negative Binomial distribution 6. Ex: Suppose when you flip a coin two times.In sample space we have 4 possible outcomes.Let X be the Discrete random Variable representing no.of Heads.Then X can take only 0,1 or 2

1. In Continuous probability Distribution the random variable can take infinite number of values in an interval is known as Continuous Ranom Variable. 2.If a random variable is Continuous random Variable then it's probability Distribution is known as ' Continuous probability Distribution'. 3.Here, The probability Density Function(PDF) is a probability distribution of continuous random variable which provides the possible values in an interval and associated probabilities.It is represented by f(X). 4.The probabilities associated with possible values in an interval must be positive and sum upto 1.For all other values the probabilities need to be zero. 1) 2) f(X) > 0 5. The following distributions are some distributions that comes under continuous probability distributions ---> Uniform distribution ---> Exponential Distribution --->Normal Distribution --->Standard Normal distribution 6.Ex: The time taken by the professor to grade a paper is uniformly distributed over [5,10] mins .Let X be the ranom variable representing the time taken by professor to grade a paper, which can take values between 5 and 10 minutes

Expected value : The expected value of a ranom variable is closely related to the weighted average and intuitively is the arithemetic mean of large number independent realizations of that variable. It is also known as ' Expectation', 'Mean' , 'Average' or First Moment. The Expected value of a random variable gives a measure of centre of distribution of the random variable .

For a Discrete probability Distribution it can be calculated by using

E[X] = =

Where X is a Discrete random variable and P(x) is it's Probability Mass Function.