Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of customers that have arrived up to time t. Let W1,W2,... be the successive arrival times of the customers. (a) Determine the conditional mean E[W1|X(t)=2].
(b) Determine the conditional mean E[W3|X(t)=5].
(c) Determine the conditional probability density function for W2, given that X(t)=5.

Step-by-step explanation:

Given that:

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

... = the successive arrival times of the customers.

(a)

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

Now

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

Now;

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

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

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation: