Let the random process X(t) be defined as X(t) = A + Bt, where A and B are independent random variables each that is uniformly distributed on [-1,1). Calculate the following: a) Mean mx(t) b) Correlation Rx(t1,t2).
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- Find the PSD of a stationary random process for which Auto correlation is Rx (t)= 6- e altiLet the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanation
- Two real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over the square whose vertices are (1, 0), (0, 1), (−1, 0), and (0, −1). Find the Correlation Coefficient ρxyQ2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the linear transformations Y₁ = X₁ + X₂, X2 + X3. Find the correlations of Y₁, Y; i, Y₂ = X₁ + X3 and Y3 for i + j. =Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure. 3₂ (0, 1) (-1,0) (a) Find Cov(Y₁ Y₂). Cov(Y₁, Y₂) = (b) Are Y₁ and Y₂ independent? Yes O No (1, 0) (c) Find the coefficient of correlation for Y₁ and Y₂. P= y/₁ (d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not? O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent. Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent. O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent. O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.(b) Let N(1) be a a zero-mean white Gaussian noise random process. Define V = N(t)dt. Find mean and variance of V.A (t) is a random process having mean = 2 and auto correlation function Rxx (7) = 4 [e- 0.2 ld+ 1. Let Y and Z be the random variables obtained by sampling X (t) at t = 2 and t = 4 respectively. Find the variance of the random variable W = Y -Z.If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.Assume that X and Y are independent random variables where X has a pdf given by fx(x) = 2aI(0,1)(x) and Y has a pdf given by fy(y) = 2(1– y)I(0,1)(y). Find the distribution of X + Y.SEE MORE QUESTIONS