What are the required conditions for a function f(x) to be a valid probability density function (pdf) of a continuous random variable X?

The commutator of matrices A and B is defined as [A, B] = AB - BA, and the anti-commutator as {A, B} = AB + BA. If {A, B} = 0, then [A, BC] can be expressed as:

For an even function f(x) defined in a symmetric interval, which of the following describes the Fourier coefficients? A. a0 ≠ 0 B. an ≠ 0 C. an = 0 D. bn = 0 Choose the correct answer from the options given below: