(a) Let (Xt)t≥o be a stochastic process defined by f fr dWr, t≥0, D where W = (Wr)rzo is a Wiener martingale and fE H. Prove rt^s € Cov(X§, Xt) = E(X¸Xt) = E [^³ f² dr, for any s,t = [0, ∞), where s ^ t = min(s, t).

Q: 26. da (x² cos y+ sin 2y) =(ry) x(- sin y y') + (cos y)(2z) + cos 2y - 2y = x-y' +y·1 = %3D %3D dx…

A:

Q: et d Calculate dt \e +1) ()

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: The two random processes X(t) and Y(t) are aej X(t) = A cos (@, t) + B sin (@n t) Y(t) = B cos (@o…

A:

Q: A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt…

A: Since, there are multiple questions. As per bartelby guidelines, only one question can be solved…

Q: 3. A random variable X has the Poisson distribution p(x; µ) = e-"µ" /x! for x = 0,1,2, .. Show that…

A:

Q: λί/λΣ=10k/μκ (1-0i-1)(1-0₁) For a multi-class M/M/1/∞/PR, show that the mean waiting time W₁ = Σi=1…

A: In a multi-class M/M/1/co/PR queue, there are r different classes of customers, denoted by…

Q: Let {N(1), t z 0} be a nonhomogeneous Poisson process with intensity function A(1), t20 However,…

A: Given that Nt, t≥0 be a nonhomogeneous Poisson process with intensity function λt, t≥0.

Q: 6. If p(r1,12) (2/3)+**(1/3)2--,(1,12) (0,0), (0, 1), (1,0). (1, 1), zero elsewhere, is the joint…

A:

Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

A:

Q: (a) Let X be a random variable with PDF ƒ(x) = 1−|x|, |x| ≤ 1. Obtain the MGF of X. (b) Find the PDF…

A:

Q: If the moment generating function of X is M(t)= 0.2+0.3(e^-t)+0.5(e^3t), then P(X>-1)=

A: Given that the Moment generating function of X is,

Q: Two random processes are defined as X (t) = A . cos (ot + 0); Y (t) = A sin (ot + 0), where A and a…

A:

Q: = 'f X is either (a) Poisson with parameter λ, or (b) (1, 2), show that the distribution of Y…

A:

Q: 1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that…

A: Given the moment generating function of the random variables X and Y :

Q: 4(x + y) 5x³ f(x, y) = Let pdf with 14]=16 then the value of A which make this probability true is…

A: Answer.     B.  1/12

Q: Find S'(-1) if #(f(x))'+ 9z°f(x) = 2 and f(-1) = 2 I'(-1) =

A: To find f'(-1) first we differentiate both sides of  the given equation with respect to x and then…

Q: 7. Let Z(x) be a stationary random function. Show that y(h) = C(0) - C(h) 8. Let Z*(x) be a…

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

Q: 2(1-z) Evaluate S S --) dy dx dz

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

Q: Why stochastic integral could be defined like So g(s) dw(s) = lim (b gn(s) dw(s) (W) (026 n->

A: Given, ∫abgs dws=limn→∞ ∫abgns dws

Q: How do i find e(x), var(x) and e(x^3) using the moment generating function

A: Let us define the random variable X with moment generating function Mx(t).The moment generating…

Q: X1,, Xn ~ N(-3,2) (random variables) ... Z, = 1(X,X2 + X1X3 + X1X4 + •..+ X1X„), n > 3 %3D (a) Find…

A: From the given information, X1, .....,Xn~N-3,2 And Zn=1nX1X2+X1X3+...+X1Xn, n≥3 Consider,…

Q: y The function f(x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree 2x

A: Follow the procedure given below.

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

A:

Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

A:

Q: Let h(t) = 3t3.2 7t-3.2 %3D | Then h'(t) is h'(1) is s! (7),.4 and h''(1) is

A:

Q: f(1) = (1' + 5z + 8) f'(z) = S'(1) = !! %D !!

A:

Q: Show that the random process X(t) = A cos (@n t+ 0) is wide-sense stationary if it is assumed that A…

A:

Q: 8. The transition probability (branching fraction) from the 3P, F = 5/2 state to the 3S, F' = 7/2…

A: Solution :-

Q: जाप) Find - 21iwy e dy ) प्रे lower bound of 101 the

A: Note: Since the given integral is with respect to dy, therefore the should be function of , .The…

Q: b) Is X(t) wide sense stationary?

A: Given That,                   X(t)=Ucost+(V+1)sint E(U)=E(V)=0 and E(U2)=E(V2)=1

Q: Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_tdt + σS_dW_t, where µ…

A:

Q: 3) Let X₁, X₂, X, be mutually independent and identically distributed exponential random variables…

A: Given that  Xi ~ E( β = 1 ) i = 1,2,3,_____,n  X1,X2,____,Xn are independent and identically…

Q: 2* f(x)= e, x = 0, 1, 2, ..., and zero elsewhere, x! show that the moment generating function of X…

A:

Q: Let (x(t)) be a Poisson process with rate A, and let T₁ = min{t: X(t) > 1} be the first arrival…

A: The first arrival time ( T1) in a Poisson process with rate (λ) is exponentially distributed with…

Q: Find the marginal distribution function of x1.x2 and eck whether they are independt are not…

A:

Q: Let S (x, y) = 4(x + y) 5x³ pdf with 14-16 then the value of A which make this probability true is…

A:

Q: f(x, y) = 6x - 2x' +3y +6xy

A: For critical points, ∂f∂x=0∂f∂y=0