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- Q2: (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. =Let Xand Y be two continuous random variables with joint probability density [3x function given by: f(x.y)%D 0sysxsl elsewhere with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10 3 E(Y*) = - and E(XY) =; %3D Then the value of the variance of 2X+Y is: O 3/80 O 91/320 43/320 7/20Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression for the correlation of XY and Y in terms of these means and variances.
- Let Y be a continuous random variable with √ ½ (2 f(y) = = Find the mean (u) and variance (o²) of Y. (2−y), 0≤ y ≤ 2 elsewhere.X and Y are two independent random variables with fy (x) eX-u (x) and fy (V) = e. u (y). Find the mean of the random variable Z= X - Y for X> Y for. X< YEX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.
- N(0, o?) is For the simple linear model Y = a + BX + €, where the error variable e ~ independent of X, use the law of total variance to show that Var(Y) = 3² Var(X)+o².Let X1, X2, and.X3 be independent and normally distributed random variables with E(X1) 4, E(X2) = 3, E(X3) = 2, Var(X1) = 1, Var(X2) = 5, Var(X3) = 2. Let Y = 2X1 + X2 – 3X3. Find 2. the distribution of Y.(b)Let X be a random variable with p.d.f, f(x)=c x=1,2,3,., zero elsewhere. Find the constant c.(b) Let X₁, X₂, X3 be uncorrelated random variables, having the same variance ². Consider the linear transformations Y₁ = X₁ + X₂, Y₂ = X₁ + X3 and Y3 = X₂ + X3 . Find the correlations of Yi, Y; for i #j. (5 marks)SEE MORE QUESTIONS