please do asap For variable X, we know that X ~ N(4,0%). If we define Y...
For variable X, we know that X ~ N(4,0%). If we define Y = log(x), then Var(Y) = (log(6)). Is this statement True or False? O True O False
If we know that E[Y|X] = E[Y], then we also know that X and Y are independent. [For those of you not used to this notation, E[Y] is the "expectation" of Y. This may have been introduced to you in another Statistics course as m or the population mean. Extending this, E [Y|X] is the expectation of Y given X.] a)True b)False
1. Let X and Y be two random variables.Then Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y). True False 2. Let c be a constant.Then Var(c)=c^2. True False 3. Knowing that a university has the following units/campuses: A, B , the medical school in another City. You are interested to know on average how many hours per week the university students spend doing homework. You go to A campus and randomly survey students walking to classes for one day. Then,this is a random sample representing the entire...
Please help!! 5 stars please step by steps and ill leave an amazing comment asap (e) A 95% confidence interval for A can be computed as [A-1 .96-Var(31), A + 1.96 Var (A)] O True O False (f) Suppose you run a regression of health status (Y) on a binary indicator for whether and individual has health insurance (X). Assuming that the sample is i.i.d. and that large outliers are unlikely, the coefficient has a descriptive interpretation. O True O...
We have a random variable, X. Using the variable, we construct a new variable Y, defined below: Y = 3X+5. Calculate the mean and variance of Y in terms of X. (i) E(Y) (ii) Var(Y)
1. Let X ~ Bin(n = 12, p = 0.4) and Y Bin(n = 12, p = 0.6), and suppose that X and Y are independent. Answer the following True/False questions. (a) E[X] + E[Y] = 12. (b) Var(X) = Var(Y). (c) P(X<3) + P(Y < 8) = 1. (d) P(X < 6) + P(Y < 6) = 1. (e) Cov(X,Y) = 0.
Let X ~ N(0, 1) and let Y be a random variable such that E[Y|X=x] = ax +b and Var[Y|X =x] = 1 a) compute E[Y] b) compute Var[Y] c) Find E[XY]
R code please Problem 3 Use a simulation to verify that when X~N(0,1), Z N(0,1)Y X3+ 10X +Z, we have Var(X+Y) Var(X)+Var(Y)+2Cov(X, Y) and Var(X-Y Var(X)Var(Y)-2Cov(X, Y). (Generate at least 50000 samples.)
N (,02). We 7. A positive random variable Y is said to be a lognormal random variable, LOGN(1,02), if In Y assume that Y, LOGN(Mi, 0), i = 1,...,n are independent. [5] (a) Find the distribution of T = II Y. [4] (b) Find E(T) and Var(T) 5) (c) If we assume that Hi = ... = Hn and oi = ... = on what does the the successive geometric average, lim (IIYA), converge in probability to? Justify your answer....
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...