# Trick or treaters arrive to your house according to a Poisson process with a constant rate parameter of 20 per hour. Suppose you begin sitting on your front porch, observing these arrivals, at some point in time. Suppose a trick or treater arrived 30 minutes ago, but there have been none since. What is the expected value of interarrival time (in minutes) from the previous trick or treater to the next one

The expected value of interarrival time (in minutes) from the previous trick or treater to the next one is 3 minutes.

Step-by-step explanation:

We have a Poisson process with a constant rate parameter of 20 arrival per hour.

This type of processes are memory-less, meaning that no matter how much time has passed form the last event, the probabilities of an arrival stay the same.

The mean interarrival time can be calculated as the inverse of the mean arrival for the Poisson process.

If the Poisson process has a rate of 20 arrivals per hour, the mean interarrival time is:

## Related Questions

I need help! Please include an explanation.

J. 144

Step-by-step explanation:

Perimeter of equilateral triangle is P = 16 + 16 + 16 = 48

Perimeter of square is P = x + x + x + x = 4x

since 4x = 48 => x = 48/4 = 12

Area of square = 12 x 12 = 144

I need help with these questions

1)10 months 2) 40 cm 3)8in

Step-by-step explanation:

1)1year =12 months

5/6year=?months

cross multiply

5x2=10

------

6x2=12

2)100cm in a meter

100divided by 5=20

1/5=20cm

2/5=40cm

3)12in in a foot

12divided by 3=4

1/3=4in

2/3=8 in

thats all the time I have for now bye

Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts?

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

Josie bought 750 bags of peanuts for $375 he intends to sell each bag for$.15 more than you paid how much should he charge for each bag

Step-by-step explanation:

Jose bought 750 bags for $375.00 Each bag cost$375/750= $0.50 He intends to sells them for$0.15 more

He should charge : $0.5 +$0.15=\$0.65

(1 point) For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt . A) Let r(t)=(cos4t,sin4t)Let r(t)=(cos⁡4t,sin⁡4t). Then r′(π4)r′(π4)= ( , )? B) Let r(t)=(t2,t3)Let r(t)=(t2,t3). Then r′(5)r′(5)= ( , )? C) Let r(t)=e4ti+e−5tj+tkLet r(t)=e4ti+e−5tj+tk. Then r′(−5)r′(−5)= i+i+ j+j+ kk ?

(a)

(b)

r'(5)= (10,75)

(c)

Step-by-step explanation:

(a)

Give that,the position vector is

r(t) = (cos 4t, sin 4t)

Differentiating with respect to t

r'(t) = (-4sin 4t, 4 cos 4t)    [  and   ]

To find the , we put

=(0, -4)

(b)

Give that,the position vector is

r(t) = (t²,t³)

Differentiating with respect to t

r'(t) = (2t, 3t²)

To find r'(5) ,  we put t=5

r'(5) = (2.5,3.5²)

= (10,75)

(c)

Given position vector is

Differentiating with respect to t

To find r'(-5) ,  we put t= - 5 in the above equation

For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt  are:

To compute the velocity vector, we need to find the derivative of the position vector with respect to time (t). This will give us the tangent velocity vector.

A) Let r(t) = (cos⁡4t, sin⁡4t).

To find r'(t), we take the derivative of each component with respect to t:

r'(t) = (d/dt (cos⁡4t), d/dt (sin⁡4t))

r'(t) = (-4sin⁡4t, 4cos⁡4t)

To find r'(π/4), we substitute t = π/4 into r'(t):

r'(π/4) = (-4sin⁡(4(π/4)), 4cos⁡(4(π/4)))

r'(π/4) = (-4sin⁡π, 4cos⁡π)

r'(π/4) = (0, -4)

B)

To find r'(t), we take the derivative of each component with respect to t:

To find r'(5), we substitute t = 5 into r'(t):

C) Let

To find r'(t), we take the derivative of each component with respect to t:

To find r'(-5), we substitute t = -5 into r'(t):