Probability distribution

Probability distribution means the probability a random variable has. According to the type of a random variable the name changes.

Type of X	f(x)
Discrete	pmf(probability mass function)
Continuous	pdf(probability density function)

• Mass = Density * length (in one dimension)

• Mass = Density (in zero dimension)

$$(a) \; f(x)=3(1-x)^2, 0<x<1, zero \; elsewhere \\ F(X=x) = \int_0^xf(t)dt=\int^x_03(1-t)^2dt=-(1-t)^3|^x_0=1-(1-x)^3$$

$$(b) \; f(x)=1/x^2, 1<x<\infty,zero \; elsewhere \\ F(x)=\int_1^xf(t)dt=\int_1^x1/x^2dx=-1/t|^x_1=1-1/x$$