Probability Distributions – Finite RV’s Random variables first introduced in Expected Value def. A finite random variable is a random variable that can.

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Presentation transcript:

Probability Distributions – Finite RV’s Random variables first introduced in Expected Value def. A finite random variable is a random variable that can assume only a finite number of distinct values Example: Experiment-Toss a fair coin twice X( random variable)- number of heads X can assume only 0, 1, 2

Probability mass function

Probability mass function(p.m.f)- Small f

Cumulative distribution function(c.d.f)

Cumulative distribution function(c.d.f)- Big F

Calculating Probabilities-Using p.m.f & c.d.f

p.m.f

Expected value –Finite R.V

Probability Distributions – Continuous RV’s

Probability density function-p.d.f

p.d.f

Relationship between Probability & Area of p.d.f - for Continuous R.V

Important

c.d.f

Uniform random variable

p.d.f for uniform random variable

c.d.f for uniform random variable

Expected value for uniform random variable

Example for Uniform random variable

Graph of p.d.f for uniform

Graph of c.d.f for uniform

Exponential random variable

p.d.f/c.d.f/ expected value – Exponential random variable