Handout #4

Date:

Continuous Random Variables� (CRVs)

CRVs can be used to describe random phenomena in which the variable of interest can take on any value in some interval.

We have seen DRV where they are represented by probability distributions.� CRVs are described by cumulative distribution functions, CDFs.

F(y₀) = P(y <= y₀)

So, the CDF is an increasing function.

A probability density function, PDF, is the area under the curve for a given value.

PDF:

f(y) = (d F(y))/dy

f(y) >= 0

� f(y)dy = F(�) = 1

Note: �P(a < y < b) = � f(y) dy for a to b, and a and b are constants.

Exercise:� Note:� c is a constant.

f(y) = c(z � y) if 0 <= y <= 1, and 0 elsewhere

Find the value of c.

Find CDF, F(y)

Compute F(0.4)

Compute P(0.1 � y � 0.6)