You can compute both the mean and second moment directly using the density function; in this case, it's
Then the mean (first moment) is
and the second moment is
The second moment is useful in finding the variance, which is given by
You get the standard deviation by taking the square root of the variance, and so
The value of the cosine function is -0.385
<h3>How to determine the measure of the cosine function?</h3>The figure that completes the question is added as an attachment
From the figure, we have the following sides
AB = √13
AC = 3
BC = 2
The triangle is a right triangle.
The angle B is calculated as:
cos(B) = 2/√13
Evaluate
cos(B) = 0.5547
Take the arccos of both sides
B = 56.31
This means that:
cos(ABC) = cos(56.31)
Multiply ABC by 2.
So, we have:
cos(ABC * 2) = cos(56.31 * 2)
Evaluate the product
cos(ABC * 2) = cos(112.62)
Evaluate the cosine
cos(ABC * 2) = -0.385
Hence, the value of the cosine function is -0.385
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