Discrete random variable

Discrete Random Variables

• A Discrete Random Variable is one which can only assume a countable number of values.
• These values are usually integer values, such as the number of heads when tossing a coin or the number of defective items in a batch.
• Each outcome of a discrete random variable is associated with a probability.

Probability Mass Function (PMF)

• The Probability Mass Function (PMF) of a discrete random variable is a function that gives the probability that the variable is exactly equal to some value.
• For all discrete random variables, the sum of the probabilities for all possible outcomes must equal to 1.

Expected Value (Mean) of a Discrete Random Variable

• The expected value or mean of a discrete random variable is the long-term average or most likely value of a discrete random variable.
• It can be calculated by multiplying each possible outcome by its respective probability and summing all these values.

Variance of a Discrete Random Variable

• The variance of a discrete random variable measures how far the numbers in the data set are spread out.
• Variance is calculated by finding the mean of the squares of the deviations.

Cumulative Distribution Function (CDF)

• The cumulative distribution function (CDF) of a discrete random variable provides the probability that the variable will take a value less than or equal to a particular value.
• The CDF can be found by summing up the probabilities of all outcomes less than or equal to the given value.

Understanding Discrete Random Variables and their applications are essential in your pursuit to master Probability and Statistics. Keep revising and practising!