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handout 8 - Handout 8 Chapter 6 The Normal Distribution...

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1 Handout 8. Chapter 6 The Normal Distribution . Continuous random variables can assume the infinitely many values corresponding to points on a line interval. (Think of a discrete random variable whose range of values becomes denser and denser.) Examples: Heights, weights ,length of life of a particular product • The probability distribution becomes approximately a smooth function. This is called the probability density function, f(x). d a r y p o i n t o f s o m e c l a s s , Suppose that the birth weights of 100 babies are recorded Recall: The total area under the histogram is 1. the data grouped in class intervals of 1 pound Next, we suppose that the number of measurements is increased to 5000 and they are grouped in class intervals of .25 pound. The probability density function f ( x ) describes the distribution of probability for a continuous random variable. It has the properties: 1. The total area under the probability density curve is 1. 2. P [ a X b ] = area under the probability density curve between a and b . P( a<X<b)= P( a X b) = P( a < X b) = P( a X < b) . 3. f ( x ) 0 for all x . With a continuous random variable, the probability that X = x is always 0. It is only meaningful to speak about the probability that X lies in an interval.

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handout 8 - Handout 8 Chapter 6 The Normal Distribution...

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