Let X₁,..., Xn,... (a) Prove that SA (X) = (X₂)² is consistent for . (b) Prove that dB(X) = (X₂)² - 02/n is consistent for p. ~ iid N(0, 2), where o2 is known. We wish to estimate = 0².

Q: c. - f'(1) = (3e³ – 2p¹³) In (5p¯² — *√p) -

A: To differentiate the given expression f′(1)=3e3−2p−1/3ln(5p−2−p−1/4), we'll need to apply the chain…

Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

A:

Q: Let f(x) 11 In(x). Then f'(x) is andf (8) is f"(2) is and f(8) is

A: Use differentiation for finding the values

Q: f(z +

A:

Q: 3. Please prove[x"In(x)] = x¹Jn-1(x) and [x"n(x)]= -x¯¹]n+1(x) dx

A: (.) We have to prove,(.) Bessel's functions  is given by,

Q: Let X=(1,0, – 1, -/2)'. Then, ||X||=v2 Select one: True False

A:

Q: If n = 18, then the interval of the form (- t(n-1), alpha/2 , t(n-1), alpha/2), that contains 99% of…

A: From the given information, number of observations n = 18. Confidence level  Level of significance

Q: 6x2+5 If f(x) = In x4/5 find f' (x).

A:

Q: Prove that = eika F (k) dk = F-1 {F (k)} 1 (a) ƒ (x) = (b) F [f (ax – b)] = eikb/a F (k/a).

A: 7. The problems related to Fourier transform are solved as shown below.

Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

Q: Maximise the function f(x, y) = 4xy² subject to r + y? = 2.

A:

Q: Show that 1 < arg (z).

A: Inequality - A statement of an order relationship—greater than, greater than or equal to, less…

Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

A: Given,

Q: Differentiate the function L(k) = cosh¯' (/T+ k² ). O (k² + 1)-1/2 O 1+ k2 1+k

A: ddkcosh-11+k2

Q: 7 Find the most general function F such that F'(): - 5V?.

A:

Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

A:

Q: Let h(x) = In[(f(x))² +1. Suppose that f(1) = -1 and f' (1) = 1. Find h'(1).

A:

Q: (LO16) Find all of the zeros of f (x) = x³ – 4x² + 2x + 4. A) x = 2, x = 1 ± i C) x = 2,x = 1+ V3 B)…

A: If you like the solution then please give it a thumbs up.. The Answer is:       x=2,x=1±3 So, Option…

Q: Find the area of each circle, given the radius r or the diameter d. Leave your answer in tems of t.

A: See the detailed solution below.

Q: Let 7(t) = Find 7'(t) 7 (t) =

A: Topic - vectors and derivatives Since r→t = 5 t5-1, -e-t, -3 sin2t we to find r→'t  derivative of tn…

Q: . The average value of f(x)=√(4-x^2) on [-2, 2] is 1/2 True False The function f(x) * f(x) = x² + 1…

A:

Q: Let X ~ Gamma (8, 2) . Then E |[X²] is equal to

A:

Q: let X~N (20,0.36), if P(X<b) then the value of bis = 0.05

A: X~N(20,0.36) Mean(μ)=20 standard deviation(σ)=0.36

Q: Suppose X₁ and X₂ have the joint par f(x1, x₂) fw (w) For constants w₁ > 0 and w₂ > 0, let W = W₁X₁…

A:

Q: Suppose that P(A)=0, P(C|A) =0.006, and P(C'|A')=0.0055 Find P(A∣C).

A: GivenP(A)=0P(C|A)=0.006P(C'|A')=0.0055

Q: Let ø be a C' function, and suppose 00 $(x) = >, b,Un(x)., ø"(x) = ), cnUn(x). %3D n=1 =1 Express…

A: Here in the question it is give that ϕ is a C1 function .  Consider the given function as follow:…

Q: Let {X} be i.i.d. such that X₁~ Pa(4, 1500) and suppose that N(2) ~ Po(100). Find E[S(4)] and…

A: Given that  be iid. such that  and

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: 3 2x 11-8 n x³ + 1/ 5 where [ ] = G.I.F If lim /2n dx = k, find the value of [1] + 2013.,

A: Solution :

Q: Let f(x) = x' - 5æ + 7x- 4x 3. Then f'(x) is f'(1) is f"(x) is and f''(1) is

A: Given: f(x) = x7-5x5+7x3-4x-3

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

A:

Q: If you are asked to find L4 for f(x) = edz) + In(x) on the interval [2,10], what would the value of…

A: From the given problem:   fx=e3x2+lnxa,b⇒2,10   As we know that the expression for the step size is:…

Q: Find the c in the MVT for f(x) = 5x-x2 , 1< x < 5. You might recall the MVT says that there is a c…

A: Consider the provided function, fx=5x-x2,1≤x≤5 Apply the mean value theorem. f'c=f5-f15-1.  Find the…