Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

Q: 9. Show that exp(iz) = exp(iz) if and only if z = nл (n = 0, ±1, 2, ...). (Compare

A: To prove that exp(iz)¯=exp(iz¯) if and only if z=nπn=0, ±1, ±2, . . ..

Q: A) L{t//4} : (5/4)! a+5 B) L{u-2(t)} C) L{e"u(t)} 8- 5 3! D) L{t*e"} = E) e{icm (;)} 5Cos s(s – 2)…

A: A is false  B is false  C is true  D is false  E is false  The detailed solution is as follows…

Q: Which of the following is not true for the differential operators A, B, and C? A (A+B) +C = A+ (B+C)…

A: Differential operator

Q: Determine if the ODE (1+ x*)y' + y = e² is linear or not. O linear O nonlinear

A:

Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: Let z = e**y* , x = tan¬²(st5) and y = əz Evaluate as (2s+t)²* Select one: O a. 2xy³e{x³y?} t5 t –…

A: Given,

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

A:

Q: f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂ (2) for x = 1, y = 1,2 then x and y are: dependent O…

A:

Q: (1) Let X1 ~ B(n1, p). X2 ~ B(n2,p). By mgfs show that X1 + X2 ~ B(n1 + n2,p) when X1 , X2 are…

A: Given :  x1 ~B(n1,p) x2~B(n2,p) where x1 and x2 are independent.

Q: It x~N(μ,σ"), then ²~. Option 2 ption 1 *** *** *** N(0, 1) G(1⁄2,2) x² (2)

A: Given, if x~Nμ,σ2 Then x-μσ2

Q: 2) Let f be a (1:1) Pinction such that differenhable f(3) = 7 P(7) = 8, f'(3)=2, P(1) -3 If glad = f…

A: topic - derivative of inverse function if f(a)=bg(x)=f-1(x)then g'(b)=1f'(a)

Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where x s player i's…

A:

Q: Boolean Algebra X. (X' + Y ) is equal to: O X.Y O X+Y O X.X'+X.Y O X.X'

A:

Q: 1 1 LGt-5- At²est + Ceisinh Dt = [(s – 1)3 ' s² + 2s – 5]

A:

Q: When the null hypothesis is rejected, then:    A. F>F(α,n-k,k-1)  B. F>F(α,k-1,n-k)  C. F = 0  D.…

A: We will find the rejection region in ANOVA table.

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: Prove that if m is a positive interger, l'(-m+) = 1.3.5..(2m -1)

A:

Q: Let f(x) = 1+ VI-1, then f 1'(x) = %3D Select one: O a. (r +1)2 +1 of O b. (z - 1) -1 O c (x – 1)² +…

A:

Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: 3. (3y² + xcos xy) sh a) d) al + (3x2 + ycos xy) = 0 dx y + sen xy + x³ = 0 y2 + sen xy + x³ = 0 y²…

A: The given equation is;  (3y2+xcosxy) dy/dx +(3x2+ycosxy) =0

Q: Prove that cos x cos y ≤ x - y for all x, y = R.

A: Mean value Theorem : Let a function  f:[a,b]→ℝ be such that    (i) f is continuous on [a,b] (ii) f…

Q: Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i)…

A:

Q: show that 11 1+ 1 n-1 1 n(ā-μο)2 Σ=1(xi-x)2 n/2 n(ā – μο)2 Σ=1(α; - z)2 (xi

A: We need to prove that:

Q: Let z(x, y) = xe* + sin xy + y - In 2 then a a) -In 2-2 b) In 2-2 2 c) 2 (²-1) d) - 2 (²+1)

A:

Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

A:

Q: O a. 1-1/e O b.0 O c. 1+1/e O d. Divergent O e. 1

A:

Q: 13 |X + 3 1 O A. [ at2 + bt + c° dt2 + et +f O B. at + b ct + d O C.[ at2 + bt + c dt + e

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the missing parts of the Wronskian: x Inx ? W = inx - and 4 O x2Inx and x3Inx O 1 and Inx O 1…

A:

Q: #9 Recently, six single-family homes in Corpus Christi in Texas sold at the following prices (in…

A: Given,Sample size(n)=6sample mean(x)=589.5standard deviation(s)=86.2549degrees of freedom…

Q: 2(x-1) If y = Vx² – 2x then y' 3x2-2x

A: For the first part, we differentiate the given function y with respect to 'x' and use change rule of…