Compute the joint pdf of random variables Y₁ = X₁ and Y₂ = X₂.
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- X is a Poisson random variable with a rate 11 Calculate P(X = 8)?Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter e > 0 is defined by F(x; 6) = 1-e x>0 (8) i) What is the variance of X,V (X)? (7)Suppose that a random variable X is an Exponential Random Variable with parameter β = 3.(a) What is E(X)?(b) Compute P(X > 2).(c) Compute P(X > 5 |X > 3).
- Suppose that X and Y are unknowns with E ( X ) = 10, Var ( X ) =4, E ( Y ) = 12 and Var ( Y ) = 100. In addition, suppose that the correlation coefficient of X with Y is .8. Then what is the expected value of XY?[Joint PDFS will be covered in Week 7] Let the random variables X and Y be the portions of the time in a day that two alternative routes between Topkapi and Uskudar have congestion (X for Route 1 and Y for Route 2). The joint PDF is given by fxy(x.y) = 2x2 + y? where Osxys1. (b) Assume Z=X+Y and W= XY and traffic experts are interested in the expected values of Z and W. E(Z) = and E(W) =O (Simplify your answers. Do not convert fractions into decimals.) (c) Find the variances of X and Y as well as the covariance between them. v(X) =D VY) =D and Cov(X, Y) =D (Simplify your answers. Do not convert fractions into decimals.) (d) The variance of Z can be found as V(Z) =- (Simplify your answer. Do not convert fractions into decimals.)Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4