PLEASE HELP! doing a test!

Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of custom

mash [69]

Answer:

Step-by-step explanation:

Given that:

X(t) = be the number of customers that have arrived up to time t.

$W_1,W_2$ ... = the successive arrival times of the customers.

(a)

Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;

$E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))$

$= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}$

$= 1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}$

$= 1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}$

Now $P(X(s) \leq 0) = P(X(s) = 0)$

(b) We can Determine the conditional mean E[W3|X(t)=5] as follows;

$E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\ = 1- P (X(s) \leq 2 | X (t) = 5 ) \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}$

Now; $P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)$

(c) Determine the conditional probability density function for W2, given that X(t)=5.

So ; the conditional probability density function of $W_2$ given that X(t)=5 is:

$f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 ) \\ \\ = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)$

7 0

4 years ago

Emily gets 9n a Ferris wheel at its lowest point which is 10 feet above the ground. She notices that she is 50 feet above the gr

navik [9.2K]

Answer:

Step-by-step explanation:

divided all the number

3 0

3 years ago

Help! can someone please give me the answer

AlladinOne [14]

<h2>I can't answer your question, but please mark it as brainliest</h2>

Pliss

7 0

3 years ago

Read 2 more answers

FInd the solution for 4(x - 5)=2(x - 10) +2x

crimeas [40]

Hello!

You solve this like an algebraic equation

You first distribute the 4 and 2

4x - 20 = 2x - 20 + 2x

Combine like terms

4x - 20 = 4x - 20

subtract 4x from both sides

-20 = 0x - 20

Add 20 to both sides

0 = 0

This means that there are infinite solutions to the equation.

Hope this helps!

3 0

4 years ago

Read 2 more answers

What is x+54 +3x+28+90 I really need help

Lesechka [4]

Answer:

4x+172

Step-by-step explanation:

x+54 +3x+28+90

Combine like terms

x+3x + 54+28+90

4x + 172