Let X1,., X, N(u, o?). iid N(H, o?). Find E(), if ju = X1 + (X2 + + X(n %3D 2(n-3) 17 16 4 O 17(n-2) 16(n-3) 17 None

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

A:

Q: 2. Golve the pollowing uaing methods for non- exad ea vations, Jintar eouaton or Bernonlli's es…

A:

Q: In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a…

A: Given that,In PCA, we obtain z∈Rk from x∈Rn as follows:z=|u(1)| |u(2)| ...…

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

A:

Q: Q2) Let X, Y be i.i.d with binomial PMF. Find PMF ofU= X+Y and W = X-Y.

A: Dear student, If you find this solution helpful please upvote ? it.

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: Let n e N, s > 0, a > 1. Show that n! 1"e" dr sn+1 Inz dr 1 (a – 1)2

A:

Q: Q #2 Let X - R" and ne N and z = 3 X,.G V neN where Gn = { (miy) €R* : y>nuf. gs z a topoligy on X.…

A: Topology means it should satisfy 3 conditions  Empty set and whole set should belong to tau.…

Q: Evaluate e2z for z Ti. 1+i 1

A: In the given problem we have to evaluate…

Q: Let z z'y- zy?, z = e ",y = e", then which of the following is ? 3012 O a. 2e- 2e 24 O b.0 Oc-2e-2e…

A:

Q: Let U1, U2, U3, .,U48 be independent and identically distributed U,~Unif(0,1) and X = U, + U2 + U3 +…

A:

Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: {o, c, s}. Find two values of c in (0, 5) such that Uf (P) = 21. %3D Let f (x) = x on [0, 5], and…

A: Given : f(x) = x on [0,5] Partition of the interval P = {0 , c , 5 }. Uf(P) = 21

Q: 2. If A C B, then m*(A) < m*(B). 3. If A = Q' n (0,1), then A is measurable. %3D

A:

Q: (a) Let U~ uniform[0, 2], and let U S= Se Find (i) E[S], (ii) P(S≥ 0.5). (b) Repeat (a) if U~ exp(2)…

A: Given: S= ∫0Ue-sds

Q: Let S= (-2, 3]U(4,5). The largest possible value of E SU such that Select one:

A: Given: S = {-2, 3} ∪{4, 5}   To find:  The largest possible value of ε &gt; 0

Q: 5. For a population with u = 80 and o= 10, what is the X value corresponding to z=- 2.00? %3D %3D

A: Givenμ=80,σ=10, Z=-2Z score=X-μσ X=?

Q: O let X be fe VrV Finel ECX) ael E(x)

A: Note: As per guidelines we can answer only one question at a time. I request you to please repost…

Q: 2. Let P: C(0, 1]C(0, 1] be given by Pp "- e. Compute dP(x). Be sure to justify your calculations.

A: Given: The given function is  P:C20,1→0,1 given by pφ=φ''-eφ

Q: evaluate Cn,x px qn-x for the values of n, x and p given below. n= 4, x=1, p= 1/2

A: The given expression is a binomial distribution with n = 4, x = 1, p = 1/2.

Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

A:

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Find the values of x and y given: m || n, m24=6z ¬5, m/10 = 5z +8, and m29 = 3y- 10. 56 87 13 14…

A:

Q: (17) Define S(n) as follows: n S(n) : i(i!) = (n+ 1)! – 1 i=1 Prove Vn e N1, S(n).

A: Consider the given expression. Sn=∑i=1nii!=n+1!-1 Now, use the mathematical indication to prove the…

Q: (10) If H < Z» × S, with |H| = 12, then H = %3D

A:

Q: 2. Let X~N(u, o2). Show that the MGF of X is etHtc²a².

A:

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: 3 For f(x,y) = In x+y°, 4,8)

A:

Q: (X,) is a sequence of independent identically distributed positive RVs, where E(X,) = a and EX,'=b…

A:

Q: 3 II vcos (=") dz dy dz Evaluate 0,

A: Then given integral is  ∫01∫0z2∫03ycosz5dxdydz

Q: The RCBD additive model is given by: A. i = n +3+T+eu B. = Hi +3+eu C. Y = Hi+n D. Yi =1+3, + Te +…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: For any k = 1, 2, .... n, find E T₁+T2+ T₁+T2+ ... + Tk + In,

A:

Q: Let X be N(0, 1)and Y be N(0, 9) , with X and Y independent. Let Z 2X – 16Y, and let W = 3X3 + 4Y5…

A:

Q: Sppose a ie ance compay ss a20.0o0 e mie tompany e The rt e Comp nd e epet e epo tem

A: Suppose a life insurance company sells a $290,000 one year term life insurance policy to a 19 year…

Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x&gt;0, r&gt;0, λ&gt;0 Y~Gammas,λ fy=λsΓse-λyys-1,     y&gt;0,…

Q: Let Y,, Y2, .., Y,~iid N (µ, o²) Find the MLES of µ,o? ....

A: Given Y1,Y2, ..., Yn~Nμ,σ2

Q: If z = x – 3y, then w = 2 Using the calculation above, mark the s

A: Linear span: Let V represent a vector space, and S=v1,v2,...,vn represent a subset of V. If every…

Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

Q: See attached

A: Differentiating both sides with respect to t, we get Now, we find critical numbers of N(t)

Q: Find the charecteristic yfalynemicl matrin g the fellewing 3 -2 e 2

A: the given matrix is: 400532-202 we have to find the characteristic polynomial of the given matrix.

Q: et f(x, у, z) %3 ху + z', Р %3D (3, 9, 1

A:

Q: Show that |Re(z)|+|Im(z)| < v2|z| for any z e C.

A: The solution is given as

Q: (E,E2 – k)z(k, l) = 0, - (E1 – kE,')z(k, l) = 0. -

A: The given operator form is: E1E2-kzk,l=0             (1)

Q: Interpreting Pearson's r <0.2 102 O = very weak relationship stationali.

A: x 33 31 32 28 33 26 34 32 28 27 y 6 4 4 1 3 3 4 2 3 2 r =…

Q: Let C: |z – i| = 3 and I = $. dz. Then e 6z z2

A: By using Cauchy integral's formula for nth derivative.

Q: QiHw O let X be fe VV To e-w Finel ECX) aed ECx)

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

Q: Evaluate n e? dz where c:z-1=3 (z+1)

A:

Q: vative of o = P(1, 1, 1) in t 3 = Z

A:

Q: E. Let 2-(e-e(3). Shn that Zy-4(xe ye")=2.

A:

Q: Im e Z, Vn E Z,m = n + 5 Vn E Z, 3 X C N, \X| = n

A: on solving these statements with the help of an example we will get

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.