Consider a birth and death process, X = {X(t)} : t ≥ 0 with the 4 states, S = {0, 1, 2, 3} and instant rates per hour are specified implicitly as follows: 1 /λk = 10 minutes for (0 ≤ k ≤ 2) and 1/ µk = 30 minutes for (1 ≤ k ≤ 3) Assume that λk = 0 for k ≥ 3 and µk = 0 for k > 3. a) Derive the limiting distribution, lim t→ ∞ P [X(t) = k] for all k b) Evaluate expectations in minutes for departure times, E [S1 |X(0) = 0] and E [S3 |X(0) = 3]

Q: If F(x) = f(g(x)), where f( – 4) = 9, f'(– 4) = 6, ƒ' (2) = 1, g(2) = – 4, and g'(2) = 8, find…

A:

Q: If f' (7) = 0 and f"(a f has Select one:

A:

Q: . For each F(s) = L{f(t)}, find f(t) = L-!{F(s)}. %3D 1 a. F(s): s2 – 7s + 10

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

Q: 9. What is the maximum value of |Log z| |2| 1? on

A:

Q: Suppose that the demand D for commodity is estimated to be -0.280.34 D = Ap,m" (A+0) where p, is the…

A: (a) The price elasticity of demand is defined as the ratio of percentage change in Demand and…

Q: MCQ 2_ 0.25e-2 + 3 grams 0.25e-1 grams O -8e-1+ -1 + 10 grams -8e-2 + 10 grams

A:

Q: What type of critical point is located at x =-6, if ƒ '(x) = (x – 2)(x + 6)?

A: This question is based on application of derivative.

Q: Given f'(x) = 5e* + 8x and f(0) = 2 find f. %3D

A: We are given that f'(x)=5ex+8x and f(0)=2. So,

Q: Differentiate. F(x) = (6x + 1)? %3D F'(x)= %3D

A:

Q: 5) Suppose the function C(1), where trepresents the number of months from January 1, 2020,…

A: Given, C(t)  represents the energy cost to a manufacturing company, where t is the number of months…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(9) = 13, f(13) = 3, f'(13) = 12, f'(9)…

A: Given: Let F(x)=f(f(x)) and G(x)=(F(x))2 And f(9)=13, f(13)=3, f'(13)=12, f'(9)=10

Q: 2 Find f such that f'(x) = f(9) = 20. f(x) =O

A: Topic - integration

Q: If f(1) = 4 and f '(x) ≥ 1 for 1 ≤ x ≤ 4, how small can f(4) possibly be?

A: If a function is continuous on some closed interval  and differentiable on the open interval  then…

Q: S-2 Given: F (t) = L-1 , Find: F(3T) s(s² +1) O - 2 O 4 O - 4

A: Given :     F(t)  = L-1s-2ss2+1

Q: Suppose that the net energy generated by a solar panel in a small town up to time t in a day…

A:

Q: dx Suppose 10 = x + y' and both y = f(x) and x = g(t). If = 2 when x = 1 and y = 3, %3D dy when x =1…

A:

Q: a) Let f(x) = 2/x+3. Find the average rate of change of f(x) from x = 4 to x = 4.5 ) Let f(x) =…

A:

Q: After the function f (z) was carefully differentiated, the function f'(z) = 5- In(2) - 2 resulted.…

A:

Q: A function has a relative maximum at (-1,3). Which of the following could have been the test results…

A:

Q: In Chapter 1, we saw that an object with position function s(t) has an average velocity on the…

A: As we know The average velocity on interval  for position funtionThe average value of its velocity…

Q: ++x* +3x +4x-x-2 Fx + G В Dx +E Given: + -+ %3D x +1 (x +1)* 3 x'(x+1) Find A ,B, C, D ,E, F, and G

A: Given x6+x5+3x4+4x3−x−2x3(x2+1)2=Ax+Bx2+Cx3+Dx+Ex2+1+Fx+G(x2+1)2

Q: If ƒ(t) = (t² + 2t + 2) (3t² + 5), find: f’(t) = ƒ'(5) =

A: given,  f(t)=(t2+2t+2)(3t2+5)

Q: 10) Given f'(x) = 3x+ 2x + 1 and f(1) 4, determine ƒ(x). %3D %3D

A: Given f'(x)=3x²+2x+1....(i) and f(1)= 4...(ii)

Q: 3. The function f(x), g(x) and h(x) are shown below. What is the average rate of change of the…

A:

Q: Suppose that P(A) = 0.47, P(C | A) = 0.007, and P(C' | A') = 0.0105. Find P(A L C).

A:

Q: The force of interest, X, at time ,t, is given by X(t) = 0.02 for 0 < t< 5 and X(t) = 0.05 for t ≥ 5…

A: To calculate the present value of a payment stream, you can use the formula for the present value of…

Q: If you are asked to find L4 for f(x) = edz) + In(x) on the interval [2,10], what would the value of…

A: From the given problem:   fx=e3x2+lnxa,b⇒2,10   As we know that the expression for the step size is:…