Random Variable and Probability Distribution

In this class, We discuss Random Variable and Probability Distribution.

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The reader should have prior knowledge of probability basics. Click Here.

Focus much on the concept. The probability distribution is used much in data science and analysis.

Random Variable: A random variable is a function that assigns a real number to each sample point in the sample space of a random experiment.

Random variable denoted by X

The value present in the random variable X. is given by small x.

X = x

We go with an example to understand the definition of a random variable.

Example:

Tossing two coins.

Sample space = {HH, HT, TH, TT}

Consider Random variable X.

X denotes the number of heads.

The random variable X contains values {0, 1, 2}

0 heads, 1 head, or 2 heads.

Range of random variable X = 0 – 2

From the definition of a random variable: A random variable assigns a value to each sample point in the sample space.

Take a sample point HH from the sample space.

The random variable assigned to sample point HH is 2.

Below are the probabilities for the random variable X = x.

P(X = 0) = 1/4

P(X = 1) = 2/4

P(X = 2) = 1/4

Another random variable Y.

The random variable Y denotes the number of tails.

Important: We can assign more than one random variable to the random experiment.

Probability Distribution or Distribution

It gives a set of possible values of the random variable X and its probability values.