2.1 Determine y(t) by deriving the Inverse Laplace transform: y(t)=L 98² (s+1)(s²+2s+10) (8) 2.2 Determine L (In t). (7) 2.3 Illustrate the convolution of independent binomial distributions of X and Y to determine the distribution of Z = X+Y. X is distributed b(n, p) and Y is distributed, independently of X, b(m, p). (4) 2.4 Using convolutions determine the distribution of X + Y if X is distributed negative binomial (r,p) and Y is distributed negative binomial (s,p), 0

Q: . Find the Z transform of : x(k) = (2)*sin,k

A: Z transform

Q: Find the Laplace Transform of the following: (2 3. h(t) = }t t 4

A:

Q: Determine the inverse Laplace transform of Fisi= (s+1)(s+2)

A:

Q: Advanced Math Find the transform X(z) of the discrete function: x(k) = Sk4, 0, KENU {0} k < 0

A:

Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

A:

Q: Find the inverse Laplace transform of F₁ (s) (s+3)2

A:

Q: Quest The moment generating function of X is given by Mx() = exp(2e - 2} and that of Y by Myt) = (e…

A:

Q: 1 1 s? +4 s -4 (s+3)

A:

Q: Show that the correlation coefficient can be expressed in the following form (show all your work and…

A:

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: Q6] What are the Fourier transforms of these two parts of the pulse? IGO|| arg|G()|| 1.0 0 27 اده 2…

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: Find the Laplace transform of e- (s+1)? s-1 (s-1)2 s+1

A:

Q: Find the inverse Laplace transform of the given function. 7! F(s) = (s – 6)* c-'{F(s)} =

A:

Q: If * represents convolution, determine the Laplace transform of f(t) = 12t * e-3t

A:

Q: Let X­­1 ~ Binomial(n1, p), and let X2 ~ Binomial(n2, p), independent of X1.  Show using a discrete…

A: It is given that: X­­1 ~ Binomial(n1, p) X2 ~ Binomial(n2, p) Y = X1 + X2

Q: Aliakbar Montazer Haghigh 118 e-s 3.5.8. F(s) = %3D s2 +9 3.5.9. F(s) = e-2s s2 + 6s +9 3.5.10. F(8)…

A: As we know that the Laplace transform  LHt-aft-a⇔e-asFs Lcos(at)⇔ss2+a2 Lsin(at)⇔as2+a2 Leat⇔1s-a…

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

A:

Q: u)n(p+u°О

A:

Q: What is the Laplace transform of: f(t)=5t+18+41²H(t-6)?

A: We have to find Laplace transform of given function.

Q: The Wigner-Weyl transform is given by 1 W (r,p) 2nh a) Proof that V(2)* = / dp W (z.p).

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 8(a) Using Convolution theorem, find the inverse Laplace transform of s2 +aP

A:

Q: Evaluate the inverse Laplace transform: 4s+1 {부

A:

Q: The Laplace transform off (t) = (t – 1)U(t – 3) is: F(s) = e ++) F(s) = e-³* (; +}) %3D -3s This…

A:

Q: (1 + e4)?

A:

Q: Find the Laplace transform of the given function; a and b are real constants. f(t) = e** sinh(bt)…

A:

Q: How can I inverse laplace transform? 3 10 (511)2(513)

A:

Q: Find the inverse Laplace transform f(t) = L{F(s)} of the function F(s) 5 2 s2 8 - 9 1) = c*{-(? 2 8…

A: We find inverse Laplace transform

Q: Draw the graph and find the Fourier transform of f(t)=e-at, a>0.

A: