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Probability Distributions – Finite RV’s

This article delves into the fundamentals of finite and continuous random variables, highlighting their significance in probability theory. It discusses finite random variables, which can take on a limited number of distinct values, illustrated by the example of tossing a fair coin twice. The article also covers essential concepts such as probability mass functions (p.m.f.) and cumulative distribution functions (c.d.f.) for finite RVs, and transitions into continuous RVs, addressing probability density functions (p.d.f.), relationships to area, and specific cases like uniform and exponential distributions.

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Probability Distributions – Finite RV’s

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  1. 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

  2. Probability mass function

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

  4. Cumulative distribution function(c.d.f)

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

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

  7. p.m.f

  8. Expected value –Finite R.V

  9. Probability Distributions – Continuous RV’s

  10. Probability density function-p.d.f

  11. p.d.f

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

  13. Important

  14. c.d.f

  15. Uniform random variable

  16. p.d.f for uniform random variable

  17. c.d.f for uniform random variable

  18. Expected value for uniform random variable

  19. Example for Uniform random variable

  20. Graph of p.d.f for uniform

  21. Graph of c.d.f for uniform

  22. Exponential random variable

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

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