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
could you help me with this question: Aspherical shell is formed by taking a solid sphere of radius 24.0 cm and hollowing out a
kumpel [21]

Answer:

La vdd tengo la misma duda, de q prepa eres?

Explanation:

Nada más para saber

5 0
3 years ago
A bird accelerating from rest at a constant rate,experiences a displacement of 28 m in 11s.What is its acceleration
Ksenya-84 [330]
Use the formula below for this question:

v_{f} = v_{i} + 2 * a * d

re-arrange to solve for a:

a = \frac{v_{f} - v_{i}}{2 * d}

now simply plug in your variables and there's your answer :). If you ever get stuck, you can look up the kinematic equations!
4 0
3 years ago
qué le sucede a la intensidad de la luz de cada bombillo en un circuito en serie si agregas más bombillos al circuito?
aalyn [17]
La intensidad de la luz se baja con cada bombillo que agregas
7 0
2 years ago
When an object moves in uniform circular motion, the direction of its acceleration is?
Harrizon [31]
Clock wise idk i think you should double check my answer

7 0
2 years ago
yesenia wants to bake cookies in her electric oven. the oven will transform electrical energy into ________ energy?
lana [24]
<span>The oven will transform electrical energy into heat energy</span>
5 0
3 years ago
Read 2 more answers
Other questions:
  • Make a list of possible consequenes of solar flares to the following members of your community
    11·1 answer
  • What steps starts the water cycle
    11·1 answer
  • A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its centre and perpendicula
    6·1 answer
  • At a certain depth in the ocean. the absolute pressure is p. If you 90 to twice that depth (treating the water as incompressible
    12·1 answer
  • A spring of spring constant k=8.25N/m is displaced from equilibrium by a distance of 0.150m. What is the stored energy in the fo
    14·1 answer
  • A scientist discovers a fossil of an animal and places it in the fossil record. The organism’s bones are similar to the bones of
    9·2 answers
  • How do you find the speed of a hraph
    9·1 answer
  • Lvl 2: Select the passage which best describes the motion of the student.
    12·1 answer
  • g 2. In a laboratory experiment on standing waves a string 3.0 ft long is attached to the prong of an electrically driven tuning
    9·1 answer
  • Gravity on Jupiter is 25 m/s/s, what is the weight of a 12 kg object on Jupiter?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!