Mean and Variance of a Mixture Recall that X follows a mixture of two Gaussians if and only if X = ZX1 + (1 – Z) X2 where Z ~ Ber (1), X1 ~ N (41,0}), X2 ~ N (42, 03) and Z is independent of X1 and X2. Assume that 41 = 0, 42 = 1 and of = o =1 and T = 1/4. Note that r here is not the constant 3.14... What is the expected value of X? E [X] = What is the variance of X? Var (X) = For the above computations, do you have to assume that X1 is independent of X2? Yes No

Q: Assume we have a linear model with 2 X variables, X1, X2. Show that the variance inflation factors…

A: variance inflation factor (VIF) : is the ratio  of the variance of estimating some parameter in a…

Q: Q. 1 Let X be a random variable with the following mass distribution P(X = x) %3D 0.3 1 0.5 2 0.2…

A:

Q: Let X and Y be statistically independent random variables with Var(X) = 4 and Var(Y) = 10. We do not…

A: The provided information is as follows:. and  are independent random variables..

Q: Let W be a plane in R³. Let P be the matrix of the projection onto W and let R be the matrix of the…

A:

Q: how would you calculate a-d of question 2?

A: We will calculate one by one in the following manner from the given data:

Q: Consider the following structural model: y1 = Bo + B132 +₂51 +21 Suppose now that there are two…

A:

Q: We know that X is an unknown distribution with a mean of u and a variance Xị are i.i.d. e

A: From the given information, X is an unknown distribution with a mean of μ and a variance of σ2; And…

Q: 4. Random Process Let X (1) be a Random process, with mean x (t) = (t-1) and autocovariance Rx (11,…

A: It is given that X(t) is a random process with mean μX(t)=(t−1) and autocovariance RX(t1,t2) at time…

Q: where M {4,., Hk}, T = {T1, 72; , Пк}, and %3D D p(x|4) = TTHi" (1 – Hki)-"n). i=1 Show that: 1. 10…

A:

Q: 3. Two dimensional random variable (X, Y) is given by X / Y 1 2 3 0,3 | 0,2 | 0,1 0,2 | 0,1 1 0,1…

A: Two events are said to be independent if the occurrence or non-occurrence of one event does…

Q: 16. Let V be a vector random variable with mean vector E(V): E(V – μν)(V – μν)΄ = Σy. Show that…

A: Given information E(v)=μv,Σv=E(v−μv)(v−μv)′

Q: True or false. • (i) –1< Cov(X,Y) < 1. • (ii) Two random variables are independent if their…

A: Statement (i) is true.

Q: If E(X) = 6 and E[(X) (X-1) ] = 51, find the second moment= 1 and the variance of X= 2

A: Given Data: E(X)=6 E[(X) (X-1)]=51

Q: The joint pmf for X and Y is given in the accompanying table. (1) Find the marginal pmf's for X and…

A: The joint pmf for X and Y is given in the accompanying table

Q: Statistic question for signals please help. Let Z(t)=X(t)+Y(t), where X(t) and Y(t) are independent…

A:

Q: amples of 2 units will be selected from the population whose distribution is given below, with a…

A: Sample of 2 units selected with replacement and order of the sample matters than the total number of…

Q: ΣX2 = 65        ΣY2 = 54100                       X̅ = 2.3        Y̅ = 73…

A:

Q: uppose X and Y are independent random variables. If the pdf of x is xe ",x ≥ 0 and the pdf of y is…

A: Solution

Q: 1. Suppose that you have the following model and data to estimate the following equation Nobs YX,X,…

A: Excel Procedure: Enter X2, X3 and Y data in Excel Go to Data Click on Data Analysis&gt;…

Q: Let X1, ..., Xn be iid N (µ, o) and suppose we are interested in estimating t(µ, 0) = o². The…

A: Since there are multiple questions we will answer the first one. Introduction - Normal distribution…

Q: 10. Two variables x and y have zero means, the same variance o and zero correlation, show that x cos…

A:

Q: (6) Let x1, -- ,X1o N(u, o2), where µ e R and o > 0 are unknown parameters. Consider the following…

A:

Q: Random variables X and Y have the joint PMF with a constant k P(x, y) = }"0. Skxy, x = 1,4; y = 1,3…

A:

Q: ates Taylor expansion log : variance of the variable Z= HY if given by Cov(Y Y-0

A: Suppose that X and Y are two random variables having MGF  φx(s)=e2s+8s2+... φY(s)=es+2s2+... taking…

Q: a) Consider the SDE dX, aXidt + √XidW₁ for X = (X)20. How should one choose a ER such that Ze is a…

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

Q: You want to see if it makes a difference which lane to be in when there is traffic. You randomly…

A:

Q: 13. Find the MGF of a random variable whose moments are u, = (r +1)! 2". Ans Mx(t) = (1-2r) 14. If a…

A:

Q: If a random variable X has pdf ?(?) = 3/376x(1−?), 0 < ?< 1 and

A: Given pdf of X is, f(x)=3376x(1-x), 0&lt;x&lt;1 Given  y=x+1y2=x+1y2-1=x2y=dxdy Limits for Y: If…

Q: • Let X1, X2, ... , X,, be a random sample from Poi(2). Find CRLB for t(1) = 1 • t(1) = e-A

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (x-μ)² 4(0²)² condition for deriving the estimator for the variance. Consider True alog L 062 False…

A: In statistical estimation, the first order condition for deriving the estimator for the variance…

Q: #3. Let X, Y and Z be random variables with V(X) = 8, V(Y) = 14, V(Z) = 10, Cov(X,Y) = 3, and…

A: X,Y,Z are random variables with V(X) = 8, V(Y) = 14, V(Z) = 10, Cov(X,Y) = 3 and, Cov(Y,Z) = -2 X…

Q: If Y is an exponential random variable with parameter , then μ = E(Y) = 8 and o² = V(Y) = 8². The…

A: We have given that Y is an exponential random variable with parameters beta then mean = E(Y) = β…

Q: 7. If x1, x2 and x3 are three variates measured from their respective means as origin and if e, is…

A:

Q: X1 and X2 are indep N(0,1) random variables. Y1=(X1+X2)/2 and Y2={(X1-X2)^2}/2. let 1. find the mgf…

A: Given: X1 and X2 are independent N(0,1) random variable: Y1=X1+X22Y2=X1-X222

Q: (21-2₂) - do SpV/1/n1+1/2 v = n₁ + 1₂-2, 01 02 but unknown, (n-1)+ (n2₂ - 1)s n₁+n₂-2 The following…

A:

Q: ΟΥ σχ i) Find the mean and variance of the statistic T = 10 Σtwi2 Σ112,2 10 i=1

A:

Q: 2. Two dimensional random variable (X, Y) is given by Y / X 1 2 -2 0 0,25 0,5 0,25 Find the…

A: GIVEN:         X         0 1 2 total   -2 0 0 0.25 0.25 Y 0 0 0.5 0 0.5   2 0.25 0 0…

Q: C2. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition…

A: The random variables  and  are given. We have to derive the expression for the…

Q: 600L tank initially has 100L saltwater with 20g salt dissolved. In flows 3L/min saltwater with…

A:

Q: Part a If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why…

A: