Using Technology In Exercises 17-22, use a symbolic integration utility to find the mean, variance, and standard deviation of the probability density function. Then find the percent of the distribution that lies within the given standard deviations of the mean. See Example 3.
Function | StandardDeviations |
To calculate: The mean, variance and standard deviation of probability density function
The percentage of the distribution that lies within the given standard deviation 1 of the mean.
Given Information:
The provided equation is,
And the standard deviation is 1.
Formula used:
If
The variance is given by,
The standard deviation of
To find the percent of distribution that lies within one standard deviation of the mean integrate
Percentage
Calculation:
Consider the function,
For the mean of the function,
Further simplify,
For the Variance of the function,
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