What is the volume of the rectangular prism?

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

3 years ago

lavonne sold 4 times as many raffle tickets as kenneth. lavonne sold 56 raffle tickets.How many tickets kenneth sold?

Fofino [41]

Its 56 times 4 = 224

8 0

2 years ago

Read 2 more answers

Help your boy out I’m not smart;)

Mice21 [21]

Answer: It may or may not be B.

6 0

3 years ago

Read 2 more answers

EASY 7TH GRADE MATH 6 out of 8 dentists recommend crest toothpaste. In a group of 156 dentists, how many of them recommend crest

Novay_Z [31]

Answer:

117

Step-by-step explanation:

6/8 = ?/156

156/8 = 19.5

19.5 x 6 = 117

6/8 = 117/156

3 0

2 years ago

Read 2 more answers

Jordan invested $600 in a savings account. The interest rate is 6% per year. Find the simple interest earned in 3 years. Then fi

olga2289 [7]

In 3 years $108 in interest is earned

principle + interest = $708

8 0

3 years ago