Give mathematical expression forstatistical definition of entropy and statethe meaning of different terms involvedin it.

The mathematical expression for the statistical definition of entropy is given by:

H(X) = - Σ P(x) log2 P(x)

In this expression, H(X) represents the entropy of a random variable X. P(x) represents the probability of the occurrence of each possible outcome x of X. The term log2 P(x) represents the logarithm of the probability P(x) to the base 2.

The meaning of the different terms involved in the expression are as follows:

• H(X): This represents the entropy of the random variable X. Entropy is a measure of the uncertainty or randomness associated with the outcomes of X. It quantifies the average amount of information required to describe the outcomes of X.

• P(x): This represents the probability of the occurrence of each possible outcome x of X. It indicates the likelihood of each outcome happening.

• log2 P(x): This term represents the logarithm of the probability P(x) to the base 2. It measures the amount of information contained in each outcome x. The logarithm is used to scale the information in a way that reflects the binary nature of information.

By calculating the entropy using the given expression, we can determine the level of uncertainty or randomness in the outcomes of a random variable X. A higher entropy value indicates higher uncertainty and more randomness, while a lower entropy value indicates lower uncertainty and less randomness.