# Question: The phase of a sinusoid is uniformly distributed over

The phase of a sinusoid, ϴ, is uniformly distributed over so that its PDF is of the form

(a)

(b)

(c)

(a)

(b)

(c)

## Answer to relevant Questions

Let be an exponential random variable with PDF, fx (x) = e –zu(x) . (a) Find Pr (3X A random variable, , has a PDF given by (a) List all constraints on the constants a, b, and c that must be satisfied for this to be a valid PDF. (b) In terms of the constants a, b, and c, find Pr (Y >0). Suppose V is a uniform random variable, (a) Find the conditional PDF, fv|{v > 1}(v) . (b) Find the conditional PDF, fv|{1/2 < v < 3/2}(v). (c) Find the conditional CDF,fv|{1/2 < v < 3/2}(v) A random variable is equally likely to take on any integer value in the set {0, 1, 2, 3}. (a) Sketch the CDF of X fx (x). (b) Write fx (x) analytically in terms of unit step functions. Suppose X is an exponential random variable with PDF, fX (x) = exp (– x) u (x). Find a transformation, Y= g(X) so that the new random variable Y has a Cauchy PDF given byPost your question