True or False only.... 1. X and Y are independent if fx\y(¤ | y) = fy(y).2. min(X, Y) are considered as function of random variables X and Y.3. E(X + Y) = E(X)+ E(Y) only if X and Y are independent.4. In general, E(XY)= E(X)E(Y).5. Variance is always positive.6. V(м) — 07. Covariance can be negative, zero or positive.8. If X and Y are independent, then it follows that Cov(X, Y) = 0.9. If Cov(X,Y) = 0, then X and Y are independent.10. If Covariance is zero, then the correlation coefficient is 0.11. If Y = 2X, then X and Y are not independent.12. If Y — -2х, then p(X, Y) — 1.13. If X and Y are independent, then p(X, Y) = 0.14. The correlation coefficient ranges from 0 to 1.

We have given that the statements related to two random variables X and Y. Here, need to find out…

Answered: 1. X and Y are independent if fx\y(¤ |…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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?
Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…
A random sample of n1=17�1=17 securities in Economy A produced mean returns of x̄ 1=5.6% x̄ 1=5.6% with s1=2.3%�1=2.3% while another random sample of n2=20�2=20 securities in Economy B produced mean returns of x̄ 2=4.6% x̄ 2=4.6% with s2=2.3%.�2=2.3%. At α =0.2 α =0.2, can we infer that the returns differ significantly between the two economies? Assume that the samples are independent and randomly selected from normal populations with equal population variances ( σ 12= σ 22)( σ 12= σ 22). T-Distribution Table a. Calculate the test statistic. t=�= Round to three decimal places if necessary b. Determine the critical value(s) for the hypothesis test. + Round to three decimal places if necessary c. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject

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1. X and Y are independent if fx\y(¤ | y) = fy(y). 2. min(X, Y) are considered as function of random variables X and Y. 3. E(X + Y) = E(X)+ E(Y) only if X and Y are independent.