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In: Statistics and Probability

A function is odd function if f (-x) = - f(x). A function is even function...

A function is odd function if f (-x) = - f(x). A function is even function if f(-x) = f(x). f(x) = sin (x) and f(x) = x are examples of odd functions and f(x) = cos x and f(x) = e^ (-x)^2 are examples of even functions.

Give two more examples of even functions and two more examples of odd functions.

Show that for odd functions f (x), integral of f(x) from negative infinity to infinity = 0

if such improper integral exists

Show that if f (x) is odd function and f ’(x) (the derivative of f) is defined, then f ’(x) is even function.

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