Question: 7) Let W be a random variable whose conditional p.d.f. given Z=0 is the Gaussian p.d.f. with parameters =4 and 2 =3; and conditional p.d.f.

7) Let W be a random variable whose

conditional p.d.f. given Z=0 is the Gaussian p.d.f. with parameters =4 and ²=3; and conditional p.d.f. given Z=1 is the Exponential p.d.f. with parameter =0.5. Assume Z is a discrete r.v. with Bernoulli distribution with parameter q=0.9. Compute the following probabilities using MATLAB or Octave:

a) P[W>6 | Z=0]

b) P[W<0 | z=0]

c) P[W<0 | z=1]

d) P[W>2 | Z=1]

e) P[W>2]

f) P[ 0 < W < 2 ]

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