Let (X(t) : t ≥ 0) be a Poisson process of rate 2. Form a new process by deleting alternate arrivals from the process (X(t) : t ≥ 0) starting with the first (so we keep the 2nd, 4th, 6th etc.). Let (Y (t) : t ≥ 0) be the process which counts surviving arrivals. (i) Calculate P(Y (t) = 0) (ii) Determine the cumulative distribution function of the time of the first arrival in the process (Y(t) : t ≥ 0) (iii) Explain why this shows that (Y (t) : t ≥ 0) is not a Poisson process

Let (X(t) : t ≥ 0) be a Poisson process of rate 2. Form a new process by deleting alternate arrivals from the process (X(t) : t ≥ 0) starting with the first (so we keep the 2nd, 4th, 6th etc.). Let (Y (t) : t ≥ 0) be the process which counts surviving arrivals. (i) Calculate P(Y (t) = 0) (ii) Determine the cumulative distribution function of the time of the first arrival in the process (Y(t) : t ≥ 0) (iii) Explain why this shows that (Y (t) : t ≥ 0) is not a Poisson process

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

See similar textbooks

Similar questions

Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Q1: (): Let Y, ., Y, be order statistics of a random sample of size 4 from Exponential (10). Find g(yı), g(y1, Y3)and P(Y, > 100). V4-x2 Q2: (): Let f(x) = ,0 sx< 2, zero elsewhere. Let Y = 1 - Find g(y) by transformation method.
b) Let aggregate national income be given by Y; = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Ct = mY; Investment is given by Iį = i + a(Yt-1 – Yt-2) And government expenditure declines over time according to G; = Go(1 – 8)*, 0 < 8 < 1 Where d is the exogenous rate of decline of government expenditure (i) Derive the linear second order difference equation. (ii) Solve the difference equation.
How would I create a tree and find dw/dt of W = (2x-3y)/(5z-y) x = t, y = -2t, z = -3t.
6. (a) Consider a fish population, assume that the total number of fish is constant. Some of fish live in a river, some live in a lake that the river flows into. Let R(t) and L(t) denote the fish populations in the river and in the lake respectively, after t months. Suppose each month, 10% of the fish in the river move into the lake and 5% of the fish in the lake move to the river. Set up a system of differential equations for the rates of change of R(t) and L(t). Do not solve.
Find the linearization at x = a. g(x) = 20x² x − 3 L(x) = 3'a= , a = 12 (Use symbolic notation and fractions where needed.)
b) Let aggregate national income be given by Y, = C; + l4 + G Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by C = mY, Investment is given by Ik = 1 + a(Yc-1 – Ye-2) And government expenditure declines over time according to G = Go(1 – 8)', 0 < 8 <1 Where 8 is the exogenous rate of decline of government expenditure Derive the linear second order difference equation. (i) Solve the difference equation.
Let g(x, y, 2) = 0.08x + 0.01y – 0.05z - 0.06. Complete the following sentences. (a) g -Select-- by units for every 1 unit of increase in z. (b) g -Select- by units for every 1 unit of increase in x. (c) g increases by 0.01 units for every -Select-- -Select- in
Find initial value of X(s) = 10 (s+1)/(s+2)(s+6)
Suppose {Y} is a stationary process and we observe the values Y₁ = 6, Y₂ = 5, Y3 = 4, Y₁ = 6, Y5 4. Find the method of moments estimators of μ, Yo, and p₁.
Determine all the critical points for the function y = Vx²(2t- 1) O (1,1) and (1/5,-0.205) O (1,0) and (1/5,-0.205) O (1,1) and (-0.205,1/5) O (1,1) and (1/2,-0.205) O (0,1) and (1/5,-0.205)
Differentiate G(y) 1 + In(3y)