Chapter 2 continuous_random_variable_2009

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Chapter 2 continuous_random_variable_2009

  1. 1. Chapter Two Random Variable L2- Continuous random variable
  2. 2. Jan 2009 CONTINUOUS RANDOM VARIABLES <ul><li>At the end of the lecture, you will be able to : </li></ul><ul><li>describe continuous random variables </li></ul><ul><li>calculate their probability distribution and their cumulative distribution </li></ul>Learning Objectives:
  3. 3. Jan 2009 CONTINUOUS RANDOM VARIABLE <ul><li>A CONTINUOUS random variable is a random variable with an interval of real numbers for its range. </li></ul><ul><li>The probability density function f ( x ) of a continuous r.v. is used to determine probabilities from areas as follows: </li></ul>
  4. 4. Jan 2009 CONTINUOUS RANDOM VARIABLE <ul><li>The properties of the probability density function f ( x ) are: </li></ul><ul><li>If X is continuous r.v., for any x 1 and x 2 , </li></ul>
  5. 5. Jan 2009 CUMULATIVE DISTRIBUTION FUNCTION The cumulative distribution F( x ) of a discrete random variable X with probability mass function f ( x ) is
  6. 6. Jan 2009 MEAN AND VARIANCE :- Continuous R.V Mean or expected value is Variance of X is given as Standard deviation of X is  

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