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- 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 explanationSuppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?
- X is a discrete uniform (1,3) random variable. When X=x, Y is discrete uniform (1,x). (a) Find the correlation of X and Y (b) Find the mean value of X when Y=2.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
- b) A random variable X follows an exponential distribution, X~Exp(0), with parameter 0 > 0. Find the cumulative distribution function (CDF) of X. i) ii) Show that the moment generating function (MGF) of X is M(t) = iii) Use the MGF in (ii) to find the mean and variance of X.Let X be a discrete random variable with range Rx = {0, ,}, such that Px(0) = Px() = Px() = Px() = Px(*) = . Find Elsin(X). %3DThe time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let T1 and T2 be two independent waiting times for this distribution. Find expected time between each call and variance. (E(T) and V(T)) Find the probability for both T1 and T2 to be greater than one.