1. Problem 1. p.105 N 1. Let fu (x) (2-- for in some interval L. Determine L so that ,, is conjug...
Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)ds We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image tg p(s)ds
Let f(x)= if , if if a) What is the fomain of f(x)? Write in interval notation. b) Determine the y-intercept of the function, if any. Make sure to justify your answer. c) Determine the x-intercepts of the function, if any. Justify your answer. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
let f(X)=5x^3-13x^2+11x+4 if the interval of difference in 1 then cosider following statement 1. ^3f(x)=30 for all x 2. ^2f(x)=34 for x=1 3 .f(x)= 4 foe x=1 which of the statement c. if ^nO^m = ^nX^m then what is the value of O^6. what is the fun where first difference in 3x^2+7x+10 and assume h=1. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were...
Problem 5. Let E1 = Q(2,7 ), E2= (2,), 1 = 22 + 77, and 2 = 22 + 3() (i) Determine [Ei : Q] for i = 1, 2. (ii) Determine a basis of Ei over Q for i = 1, 2. (iii) Determine the minimal polynomial of i over Q for i = 1, 2. (iv) Determine if each of the extensions E1 / Q and E2 / Q is Galois. We were unable to transcribe this imageWe...
Let Y = Xβ + ε be the linear model where X be an n × p matrix with orthonormal columns (columns of X are orthogonal to each other and each column has length 1) Let be the least-squares estimate of β, and let be the ridge regression estimate with tuning parameter λ. Prove that for each j, . Note: The ridge regression estimate is given by: The least squares estimate is given by: We were unable to transcribe this...
Let V be a finite-dimensional vector space and let T L(V) be an operator. In this problem you show that there is a nonzero polynomial such that p(T) = 0. (a) What is 0 in this context? A polynomial? A linear map? An element of V? (b) Define by . Prove that is a linear map. (c) Prove that if where V is infinite-dimensional and W is finite-dimensional, then S cannot be injective. (d) Use the preceding parts to prove...
1. Let X be a discrete random variable with a cumulative distribution function: a. Use this cdf to fin the limiting distribution of the random variable when with , as n increases. Use the fact b. What kind of random variable is for large value of n? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagep= We were unable to transcribe this imageWe were unable to transcribe this imageWe were...
X1,...,Xn are IID with N(0,2). a) Determine the mean and variance for (X (subscript 1)^2) b) Show sqrt(n) * [ log ( 1/n ∑(from i=1 to n) Xi2) − log(σ2 ) ] d → N(0, 2). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. Let and . Find the eigenvalues of this matrix and determine if it is invertible. In other words, how does finding a basis of for which the matrix of is upper triangular help find the eigenvalues of and how does it help determine is is invertible? 2. Define by . Find all the eigenvalues and eigenvectors of . Note stands for either or . TE L(V) 0 0 8 We were unable to transcribe this imageWe were unable to...