Which one is better ketchup or mustard

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

HURRY PLEASE The top and bottom of a right rectangular prism are 4 inches long and 4 inches wide. What is true about the other f

Masteriza [31]

Answer:

All four of the remaining faces will be 4 inches wide.

Step-by-step explanation:

A right rectangular prism with square base and top with sides of 4 in.

It has four sides of 4 in wide each and of equal height of unknown measure.

<u>Options:</u>

All four of the remaining faces will have a height of 4 inches.

Incorrect, the height is unknown.

There is not enough information to tell what the other faces will look like.

Incorrect, all the other faces are rectangular.

Two of the remaining faces will be 4 inches wide.

Incorrect, all the faces are 4 in wide.

All four of the remaining faces will be 4 inches wide.

Correct.

6 0

2 years ago

What is 5 over20 by simplifying fraction

babymother [125]

To simplify a fraction, divide numerator and denominator by
their greatest common factor.

The greatest common factor of 5 and 20 is 5 .

5/20 = 1 / 4

4 0

2 years ago

Read 2 more answers

Lee wants to cut this piece of canvas into two rectangles that are 3x2 and 3x5. He wants the sum of the two small rectangles to

lord [1]

Yes because 3×2= 6 , 3×5= 15, 15 + 6 = 21

8 0

2 years ago

A frog is jumping onto a lily pad. Its height, h (in feet), is recorded at various seconds, t, in the

myrzilka [38]

Answer:

I don't know

Step-by-step explanation:

sorry

7 0

2 years ago