Example 3: If x1, X2 , ... , Xn is a random sample from a normal population .2 N(µ,1), show that t=- E x is an unbiased estimator of u +1.

Q: (c) lim sup (an + bn) lim inf an + lim inf bn

A:

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: If X, Y and Z are three random variables, then cov (X +Y,Z) =cov(X,Z)+cov(Y,Z)

A: Solution

Q: In this part you will show that if f(x) ≤ g(x) for all x = [a, b], then [* f(x) dx ≤ [*9(x) dx by…

A:

Q: f A is an event in the finite sample space, then prove that P (A) equals the sum of the…

A:

Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: 7. (a) V.(V4) = V²¢ (b) (4× R) _ (2-n).A n(A.R)R %3D E,r =|R|

A: a)

Q: D) Time series data: E) Population.

A: We have define the following Time series Population

Q: Prove that for every integer n > 2, P(n+1, 3) = n³ . %3D -n.

A: Given to prove that for every integer n≥2,  Pn+1, 3=n3-n. We shall prove this by the method of…

Q: The moment generating function at v = 0 is unity. It is given as M x (v )|... = Mx (0) = 1 lv 0

A:

Q: 1 Show that (tan-' x) : 1+x?

A: We use Trigonometry identities and inverse Trigonometry to solve this proof

Q: Defn "x→x*lim Xj =x' 'x; "the limit of x; is x" convenges to * " Hl proue lim 5j-l %3D

A: To understand my solution, You first go through the definition of the limit. Then you must study…

Q: Theorem 3-5. If B cA, then (i) P(AnB ) = P(A) – P(B), (ii) P(B)<P(A)

A:

Q: Compute the following. (a) P6, 2- (b) C6, 21 (c) Pa, s (d) Cg 9

A: The formula for Pn, r Pn, r  =n!n-r! The formula for Cn, r Cn, r  =n!r!×n-r! Here,  n!…

Q: Proposition 4.1.2. If ƒ : A → Rn satisfies the lower-Lipschitz condition on E, i.e., if there exists…

A: We will prove all by using the definitions

Q: (a) Let n be any integer. Prove that n2 is congruent to 0, 1 or 4 modulo 8.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: L[y''''] L[f"'''']

A:

Q: Let p(x) and q(x) be predicates with variable x. Prove the following. • (3x)p(x) (x)~p(x) I(p q) =…

A:

Q: Prove that A2=I.

A:

Q: SxY (@) = 0 and Sx (@) =0 if X(t) and Y(t) are orthogonal.

A:

Q: C. The Fibonacci numbers (Fn)n21 are defined by the recurrence F₁ = 1, F2 = 1, Fn = Fn-1 + Fn-2 for…

A:

Q: vx (P(x) → (Q(x) v R(x))), – 3x (P(x) ^ R(x)) | vx (P(x) → Q(x))

A: To prove the validity of the following: ∀x(P(x)→(Q(x)∨R(x))), ¬∃x(P(x)∧R(x))⊢∀x(P(x)→Q(x))

Q: Let S= {n | n=5 k+ 4 for some integer k} Let T= {n|n=5 j– 1 for some integer j}

A:

Q: Let a 20 be a real number (to be chosen below) and recursively define an-1 + a2-1 an = 3 for n > 2.…

A: Given that a1≥0 and recursively defined an=an−1+an−133 for n≥2.Note that the given sequence is…

Q: Prove the shown?

A: we have been given limh→0sin hh=1 and limh→0cos h-1h=0 we have to use the limits to find the…

Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: To prove the equality A - (B ∩ C) = (A - B) ∪ (A - C), we need to show that each set is a subset of…

Q: (А - B) - С - (А -C)- (В - C)

A: Introduction :

Q: An integer x is odd if x2 is odd. Let x, y and z be integers. If x y and y z, then x | z. For any…

A: