Question: 1. Let B[n] be a Bernoulli random sequence equally likely taking on values [-1, +1]. Define the random process X(t) = Vpsin 2x fot +

1. Let B[n] be a Bernoulli random sequence equally likely taking on values [-1, +1]. Define the random process X(t) = Vpsin 2x fot + B[n], fornIstti, PIN(t2 ) - N(1,] = exp -ja(v) dv , n>0 n! A(t) is called the intensity function. Compare this with a Uniform Poisson Counting Process and find a. Its mean function mean function /v(t) b. Its correlation function RAN(1,t2) 3. Let Wi(t) and W2(t) be two Wiener processes that are independent of one another with both defined for (20 with variance parameters a and o2, respectively. Define the random process given by X(t) = Wi(t) - W2(t). a. What is Rxx(t1,t2) ? b. What is the pdf fr(x;t)? 4. Let W(t) be a standard Wiener process. Define the random process X(t) = W (t ) a. Find the probability density fx(x;t). b. Find the conditional density fx(x2/x1;t2, t1)

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