1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Step2247 [10]
3 years ago
12

g (12 points) The time between incoming phone calls at a call center is a random variable with exponential density p(x) = 1 r e

−x/r on [0, [infinity]), where r = 20 ln(2). a. Verify that the function p(x) is a Probability Density Function.
Physics
1 answer:
rusak2 [61]3 years ago
6 0

Answer:

(1)p(x)\geq 0\\(2)\int_{0}^{\infty} p(x) dx=0

Explanation:

A function f(x) is a Probability Density Function if it satisfies the following conditions:

(1)f(x)\geq 0\\(2)\int_{0}^{\infty} f(x) dx=0

Given the function:

p(x)=\dfrac{1}{r}e^{-x/r} \: on\: [0,\infty), where\:r=\dfrac{20}{ln(2)}

(1)p(x) is greater than zero since the range of exponents of the Euler's number will lie in [0,\infty).

(2)

\int_{0}^{\infty} p(x)=\int_{0}^{\infty} \dfrac{1}{r}e^{-x/r}\\=\dfrac{1}{r} \int_{0}^{\infty} e^{-x/r}\\=-\dfrac{r}{r}\left[e^{-x/r}\right]_{0}^{\infty}\\=-\left[e^{-\infty/r}-e^{-0/r}\right]\\=-e^{-\infty}+e^{-0}\\SInce \: e^{-\infty} \rightarrow 0\\e^{-0}=1\\\int_{0}^{\infty} p(x)=1

The function p(x) satisfies the conditions for a probability density function.

You might be interested in
The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 54/(7 + x2 + y2), where T is measured in °C and x,
ANTONII [103]

Answer:

dt/dx = -0.373702

dt/dy =  -1.121107

Explanation:

Given data

T(x, y) = 54/(7 + x² + y²)

to find out

rate of change of temperature with respect to distance

solution

we know function

T(x, y) = 54 /( 7 + x² + y²)

so derivative it x and y direction i.e

dt/dx = -54× 2x / (7 +x² + y²)²    .........................1

dt/dy = -54× 2y / (7 + x² + y²)²      .........................2

now put the value point (1,3) as x = 1 and y = 3 in equation 1 and 2

dt/dx = -54× 2(1) / (7 +(1)² + (3)²)²  

dt/dx = -0.373702

and

dt/dy =  -54× 2(3) / (7 + (1)² + (3)²)²

dt/dy =  -1.121107

7 0
2 years ago
Provides most of the energy used in the world today.
lara [203]

fossil fuels is used the most often in the world.

6 0
2 years ago
Streak is a reliable identifier of a mineral. true or false
inysia [295]

Answer:

true?

Explanation:

Im positive but not 100% sure wait for someone else to answer and see if they say the same.

8 0
3 years ago
Read 2 more answers
If a car is moving backward and has negative acceleration, what can be said about the speed of the car?
KATRIN_1 [288]
I think its A let me know its wrong or not
4 0
2 years ago
Read 2 more answers
11. Which of the following is a proper unit of
Sergeeva-Olga [200]
D is the correct answer!!
4 0
2 years ago
Read 2 more answers
Other questions:
  • How can two objects have different mass and volume yet have the same density?
    15·1 answer
  • Steam at 4 MPa and 400C enters a nozzle steadily with a velocity of 60 m/s, and it leaves at 2 MPa and 300C. The inlet area of
    10·1 answer
  • A proton starts from rest near the surface of a sheet of charge. It experiences a force of 14.0 microNewtons towards the sheet.
    8·1 answer
  • An airplane capable of an airspeed of 100 km/hr is 60 km off the coast above the sea. If the wind is blowing from the coast out
    15·1 answer
  • Shoo the fly flaps its wings back and forth 140 times each second. The frequency of the wing flapping is ____ Hz.
    10·1 answer
  • True or false? A protostellar cloud spins faster as it contracts
    8·1 answer
  • Please help it’s urgent!
    5·1 answer
  • Give the SI unit. For physics
    12·1 answer
  • The value of acceleration due to gravity is less at the top of Mount Everest then that in the terai reason, why?​
    9·1 answer
  • You accidentally drop an eraser out of the window of an apartment 15 m above the ground
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!