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  • Random Variables

Continuous Random Variable

• Expected Value

  • $\mu =E(X)+{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}X\cdot f(x)dx$

• Unlike Discrete Random Variable, we don't need a countable support.

  • How we know from MAT102 that $(0,1)$ is infinite.

• The distribution function of a Continuous Random Variable is called a Probability Density Function ^[Probability Distribution Function] is a smooth curve

• It can have discontinuity, but it's a smooth curve.

• The area under the density is used to evaluate probability.

• The Cumulative Distribution Function of a Continuous Random Variable is a smooth curve as well. It's a non-decreasing smooth curve approaching $1$.