Find - relationship between a and b - continuous

Question

Question 1:

The probability density function is given by f_x(x) = ae^-b|x|, where x is a random variable whose allowable values range from x = -∞ to x = +∞.  Find;

(a) Relationship between a and b.

(b) Continuous Distribution Function (CDF)

(c) Probability that the outcome lies between 1 and 2.

Question 2:

(a) A white noise with autocorrelation function R_x(ζ) = δ(ζ) is applied to a linear system.

Calculate the white noise power spectral density.

(b)    Calculate the power (RMS square value) and AC power of the random signal

x(t) = V cos(wt + Φ) where V is a constant and where the phase Φ is a random variable with a uniform probability distribution over the interval [0, 2π].