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cont_distri

# cont_distri - Continuous Random Variables Suppose we are...

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Continuous Random Variables Suppose we are interested in the probability that a given random variable will take on a value on the interval from a to b where a and b are constants with a b. First, we divide the interval from a to b into n equal subintervals of width x containing respectively the points x 1 , x 2 , … , x n . S uppose that the probability that the random variable will take on a value in subinterval containing x i is given by f ( x i ) .∆ x . Then the probability that the random variable will take on a value in the interval from a to b is given by . ). ( ) ( 1 = = n i i x x f b X a P

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Continuous Random Variables (cont’d) If f is an integrable function defined for all values of the random variable, the probability that the value of the random variables falls between a and b is defined by letting x 0 as = = = b a n i i x dx x f x x f b X a P ) ( ) ( ) ( 1 0 lim Note: The value of f ( x ) does not give the probability that the corresponding random variable takes on the values x ; in the continuous case, probabilities are given by integrals not by the values f ( x ).
(cont’d)

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cont_distri - Continuous Random Variables Suppose we are...

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