Just answer these two questions quick I am VERY CONFUSED I give Brainliest

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

In the year 2000, the United States had a population of about 281.4 million people; by 2010, the population had risen to about 3

IgorC [24]

Answer:

Part 1. 0.9259 % per year

Part 2. P = 281.4e^(0.009 259t); 338.6 million

Step-by-step explanation:

Data:

P₀ = 281.4 million

P = 308.7 million

Part 1. Growth rate

t = 2010 - 2000 = 10 yr

P = P₀e^(rt)

308.7 = 281.4e^(10r)

e^(10r) = 1.0970

10r = ln1.0970

r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259

r = 0.9259 % per year

The 10-year continuous growth rate is 0.9259 % per year.

Part 2. Population model

The population model is

P = 281.4e^(0.009 259t)

where P is in millions and t is the number of years since 2000.

By 2020,

P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203

P = 338.6 million

The estimated population in 2020 is 338.6 million.

8 0

3 years ago

PLEASE ANSWER THIS I WILL GIVE YOU 7 POINTS

MissTica

Answer:

tell me the question

Step-by-step explanation:

l am ready for you

6 0

2 years ago

Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal. Who is correct and why?

shusha [124]

Answer

2.11 is rational number Hannah is correct because it doesn't have 3 dots in the end if it is repeating decimal it will be (2.11.......

7 0

3 years ago

Read 2 more answers

What is the percent increase of 24 to 32?

goblinko [34]

Answer:

8%???????????????????????

6 0

1 year ago

Read 2 more answers