Consider a branching process with generation sizes Zn satisfying Zo = 1 and P(Z₁ = 0) = 0. Pick two individuals at random (with replacement) from the nth generation and let L be the index of the generation which contains their most recent common ancestor. Show that P(L = r) = E(Z¹) - E(Z1) for 0 ≤r 0?

Q: A continuous-time signal is sampled 44,100 times per second, resulting in a sequence of values…

A: Introduction: The Z-transformation is a discrete type transformation with which we can transform a…

Q: If the sequence {gm} is orthonormal on [a,b] with weight function w(x), then the sequence {Vw (x)…

A:

Q: the difference equation y(+2)-(n+1)-(n)=x(n). -{(?). (n)= n≥o n20 and initial conditions (0)=0,…

A: The difference equation given is as follows: yn+2-16yn+1-16yn=xn,  n≥0 With, xn=12n,  n≥00,  n<0…

Q: SHOE ALL THE STEPS

A: The objective of this question is to find a recursive relation for the coefficients of a power…

Q: Let (X„) be a sequence of independent exponentially distributed random variables w respectively. log…

A: From the given information, Xn be a sequence of independent exponentially distributed random…

Q: In one plane, draw D[0, 1]\{0} (a closed “punctured" disk) along with the first three terms of the…

A: According to the definition,  D¯0,1\0=z∈ℂ:0<z≤1 Given sequences are  zn=2eiπ-π2nqn=3ei-π+π2n Now,…

Q: Find two linearly independent solutions y₁(x) and y₁(x) to y"-2xy' -2y = 0 about the ordinary point…

A: The given differential equation is:y′′−2xy′−2y=0 Now the power series solution of the given…

Q: 5) Obtain the three-point central difference formula for the second order derivative with a…

A: The formula for Taylor's series expansion about a point x0 is…

Q: determine the following values for the nth partial sumof the Fourier Series of the given…

A:

Q: The Taylor series of the function f(x)=₁x about the point x=2 is a)_ƒ(x)=[(-1)"(x-2)**² PF0 b) ƒ (x)…

A:

Q: Q3. Consider a series system of 4 independent components with failure rate functions: h,(1) = 1,…

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: у" - In x

A: Given: y''=lnx

Q: 21) f(x)=47x A) (4 ln 7)47x Write summation notation for B) (7ln 4)47x x(In 2) C) (In 4) 47x x(In x)…

A: Finding the derivative of f(x)

Q: Use the method of, logant to differentiate the fune tion thoms d fferentiation Do not use any other…

A: The solution are next step

Q: x' + 2e* – In xr- 3 = 0

A:

Q: 2- Discrete dx" using polynomials with backward differencing in equisized grid. n is one before the…

A:

Q: Does the Taylor Series Expansion of f(x)=(1+3x)^(24) about a=1 have only a finite number

A:

Q: 0 iF X Poisson (u) compute P(x=2)

A: Since both the questions are from different distributions so as per the Bartleby guidelines, only…

Q: Xn+1 = 1 converges to a solution of the equation x² + x- Xn 11 = 0, [2,3]. True O false

A:

Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: show that a RW model without drift is non stationary when doing times series

A: Given the statement that a random walk (RW) without drift is non stationary.

Q: The function f(n) = 2", n = 1, 2, 3,... %3D %3D The function f(n) = n!, n 0, 1,2,... %3D The…

A: The recursive definition of a sequence is a general formula that describes the relationship between…

Q: 5. Find the critical numbers. y= x5/3 – 3x2/3

A: