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Unformatted text preview: 3. Find the values of constants a and b such that: F X (x) = [1  aEXP(x/b)]u(x) Is a valid distribution function {note that u(x) is the unit step function} ECE757Practice Problems SOLUTIONS 4. The pdf of a random variable X is given by: ⎩ ⎨ ⎧ ≤ ≤ = otherwise b x a k x f X ) ( Where, k, is a constant. a) Determine the value of k. b) Let a = 1 and b = 2. Calculate P[X ≤ c] for c=1/2 5. Let X and Y be defined by: X=cos( Φ ) and Y=sin( Φ ), where Φ is a random variable uniformly distributed over [0, 2 π ]. a) Show that X and Y are uncorrelated b) Show that X and Y are not independent. 6. Consider a random process X(t) given by: X(t)=Acos( ω t+ Φ ), Where, A and ω are constants and Φ is a uniform random variable over [π , π ]. Show that X(t) is Wide Sense Stationary. ECE757Practice Problems...
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 Spring '09
 messner
 New Hampshire, Commmunication Systems, Commmunication Systems FALL

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