Probability Distribution Function:
Probability distribution function is defined for discrete random variables. It is a function that allocates the probability values for each event. It provides a relation to the probabilities for the values that the random variable may possess.
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Probability Density Function
Probability density function is the probability distribution function for the continuous random variables. It gives the likelihood of a certain random variable to assume a certain value.
Let X is a discrete random variable,
So the function given as f(x) = P(X = x) for each x that lies within the range of X is called the probability distribution function. A function can serve as the probability distribution function if and only if the function satisfies the following conditions.
1. f(x) ≥ 0
2. ∑ f(x) = 1
A function f(x) that is defined over the set of real numbers is called the probability density function of the continuous random variable X, if and only if,
P(a ≤ x ≤ b) = a∫b f(x) dx for any real constants a and b.
The probability density function should satisfy the following conditions too.
1. f(x) ≥ 0 for all x: -∞ < x < +∞
2. -∞∫+∞ f(x) dx = 1
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