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Chapter Two Random Variable L2-  Continuous random variable
Jan 2009 CONTINUOUS RANDOM VARIABLES At the end of the lecture, you will be able to : describe continuous random variables calculate their probability distribution and their  cumulative distribution Learning Objectives:
Jan 2009 CONTINUOUS RANDOM VARIABLE A  CONTINUOUS  random variable is a random variable with an interval of real numbers for its range.  The probability density function  f ( x ) of a continuous r.v. is used to determine probabilities from areas as follows:
Jan 2009 CONTINUOUS RANDOM VARIABLE The properties of the probability density function  f ( x ) are: If  X  is continuous r.v., for any  x 1  and  x 2 ,
Jan 2009 CUMULATIVE DISTRIBUTION FUNCTION   The cumulative distribution  F( x ) of a discrete random  variable X with probability mass function  f ( x ) is
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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Chapter 2 continuous_random_variable_2009

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