Examples of Normal Distribution
Example 1:
If the value of a random variable is 8, the mean is 10, and the standard deviation is 3, then find the probability density function (PDF) of the normal distribution at this value.
Solution:
To find the PDF at the value of the random variable (8), use the formula for the normal distribution.
According to the given information, we have, Mean (μ) = 10, Standard Deviation (σ) = 3, and e is the base of the natural logarithm (approximately 2.71828)
Now, putting the values in the formula, we get:
f(8) = 0.10648
Example 2:
If the value of a random variable is 12, the mean is 15, and the standard deviation is 2, then find the probability density function (PDF) of the Gaussian distribution at this value.
Solution:
To find the PDF at the value of the random variable (12), use the formula for the normal distribution,
According to the given information, we have, Mean (μ) = 15, Standard Deviation (σ) = 2, and e is the base of the natural logarithm (approximately 2.71828)
Now, putting the values in the formula, we get,
f(12) = 0.06475
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