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

1. Let B[n] be a Bernoulli random sequence equally likely taking on values [-1, +1]. Define the random process x(t) = psin 2nfat + B[n]? fornIstt1, PIN(t2 ) - N(t ]: n! -exp - ja(va , n >0 (t) is called the intensity function. Compare this with a Uniform Poisson Counting Process and find a. Its mean function mean function ux(t) b. Its correlation function RNM( 1,t2) 3. Let Wi(t) and W2(t) be two Wiener processes that are independent of one another with both defined for 120 with variance parameters on and oz, respectively. Define the random process given by X(t) = Wi(t) - W2(t). a. What is Rxx(t1,t2) ? b. What is the pdf fx(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; 1). b. Find the conditional density fx(x2/x1;t2, t1)

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