MATH103 April 2005
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A certain random variable X takes values in the interval , with probability density
Find the mean and variance of X.
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For a continuous probability density p(x) with mean the variance is given by
Alternatively, the variance can also be calculated by
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Given the probability density p(x)=1-x/2 over the interval we plug this into the formula for the mean to get
Using the first formula for the variance with ,
Alternatively, using the other formula for the variance, we get the same value:
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