Probability distribution and Probability Density function (pdf)

Probability distribution
Probability distribution specifies the probabilities of the possible outcomes of a random variable. There are many different classifications of probability distributions such as the chi square, and normal and binomial distributions.

Probability Density function (pdf)
Specify the probability that a continuous random variable takes on a specific value.

f(x)=P(x1≦X≦x2)=(x2-x1)/(b-a)

Notes:

• Pdf of a number is a function 0≤ p(x) <1>
• Integral over the range of the random variable equals 1,∫p(x)dx = 1

Probability function
Probability function specifies the probability that the random variable takes on a specific value: P(X = x).

Properties of probability function
· 0 ≤ p(x) ≤ 1 because a probability lies between 0 and 1.
· The sum of probabilities p(x) over all values of X equals 1.

Cumulative Distribution function
Specify the probability that the random variable X is less than or equal to a particular value x.

F(x)=P(X≦x)