4. (a) Let d > 0, and let X be a continuous random variable satisfying X - Unifl-d, d]. Calculate ox (t). Make sure to write your answer in terms of real and imaginary parts. (b) Let c, d > 0. Use the Inversion Theorem to prove that sin(ct) sin(dt) t2 dt = r min{c, d}. (Hint: this is related to part (a).)

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

A:

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: (d) Are X and Y independent? Justify your answer.

A:

Q: Let fV)= [(x sinx)*'e*sin (xcosx+ sinx)dx, y>-2. Compute S(35) y+1 Hint : Use gamma function. O A…

A:

Q: Q1 Let X1,.,X, f(r;0) = )0"(1 - 0)2-,x = 0,1,2. (i) Find the score and information functions of 0.…

A: Let, X1,x2,...,Xn be the random samples having following distribution: f(x;θ)=2xθx(1-θ)2-x  ;…

Q: Q4 Sampling at the argument values t,= 1, t= 2, ty= 3 and ty= 4 and the discrete function is fita) =…

A: Given: The argument values, t0=1, t1=2, t2=3 and t3=4 and their corresponding discrete functional…

Q: (Inx)° dx = O 1) S(nx)* + С 2) (Inx) + C 3) (In x) + C 6x

A:

Q: 2) Recall F(X = t) = Pr(X < t) calculate the following using the Z transform and F(Z=t) for the…

A: According to our guidelines we are solving only first three sub-parts of a question. Given that F(X…

Q: Let F(t) = (4t³ - 1)j + (5t+2)k. Find F'(t). 7"(t) O 288t 288t³j 05+288t³ O 36t³ +5 O None of these

A:

Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: Let 7(t) = VE + 4, cos(t), te-'> (t*), te¯t >

A:

Q: -If the wavefunction (x) = eikx Find the Normalize constant A

A: If we multiply a function which has a positive area with normalizing constant the total area under…

Q: Prove that + J2 (x) + J, (x) = 0

A:

Q: show that | | J.(x)dx x² J,(x)dx = x²J¼(x) + x J,(x) – %3D

A: Apply the integration by parts method and use the identity ∫xpJp-1xdx=xpJpx, to evaluate the…

Q: In the context of ordinary least square (OLS): Given mịn- ||Y – Xß||? Use derivatives to derive the…

A:

Q: consider che funceion h= w²-8.Tawei Determine dh/dt and w= St"-26

A:

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

A:

Q: d) Pr(|X| < a) e) Pr(|X| 2 a)|

A:

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

A:

Q: ) 3x - 4x= sin社 ; at t=0,x==

A:

Q: Integrate the function. 2+81 dx 4x2 V In Vx2 + 81 + x x2+81 4x + C In Vx2 • 81 + x] Vx2 + 81 + C 4x…

A: Given,            ∫x2 + 814x2 dx

Q: 3. The Cov(X) of a random vector X'= (X₁, ..., Xn) is defined as E{(X-E(X))'(X-E(X)}. True or false,…

A: We know that, X' is a vector and Covariance of a vector X is equal to the variance of X.  Which…

Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

A:

Q: Prove that • I %3D

A:

Q: Q1 Let X1,.,X, f(r;0) = ()0 (1 – 0)2-, x = 0,1,2. (i) Find the score and information functions of 0.…

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

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: cos ax -dx = te' 2 х* +1 ле",а 20.

A: In this context, prove ∫-∞∞cos axx2+1dx=πe-a,a≥0. Consider, ∫cfzdz=∫-∞∞cos…

Q: xt) t osh 3t sinh 3t + ws (ot - )

A: If f(t) is a function of t defined for all positive values of t. Then, the Laplace transform of the…

Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

A:

Q: In (secx) a) | sec2t dt + cot x

A:

Q: 2) Consider the sinusoidal signal x(t) =cos(500rt + 0), and suppose that this signal is sampled,…

A: please see the next step for solution

Q: 7/j=4/z+7/w j=

A: