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
777dan777 [17]
1 year ago
11

Assume that the number of messages input to a communication channel in an Exponential distribution with 7 messages arriving in a

10 second period. Compute the probability that more than 3 messages will arrive during a 30-second interval.
Mathematics
1 answer:
NARA [144]1 year ago
7 0

The probability that more than 3 messages will arrive during a 30-second interval is P(X=n)=\dfrac{e^{-0.3 \times 20} (0.3 \times 20)^n}{n!}.

According to the statement

we have given that the an Exponential distribution with 7 messages arriving in a 10 second period and we have to find the probability that more than 3 messages will arrive during a 30-second interval.

So, For this purpose, we know that the

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

And the given information is that :

3 messages will arrive during a 30-second interval.

Then

Probability = P(X=1) + P(X=2) + P(X=3).Then

The probability become according to the exponential distribution:

P(X=1)=\dfrac{e^{-0.3 \times 20} (0.3 \times 20)^1}{1!}\\P(X=2)=\dfrac{e^{-0.3 \times 20} (0.3 \times 20)^2}{2!}\\P(X=3)=\dfrac{e^{-0.3 \times 20} (0.3 \times 20)^3}{3!}\\

And then substitute the values in it then

Probability = \dfrac{e^{-0.3 \times 20} (0.3 \times 20)^1}{1!}\ +\dfrac{e^{-0.3 \times 20} (0.3 \times 20)^2}{2!}\ + \dfrac{e^{-0.3 \times 20} (0.3 \times 20)^3}{3!}\\

This is the probability.

So, The probability that more than 3 messages will arrive during a 30-second interval is P(X=n)=\dfrac{e^{-0.3 \times 20} (0.3 \times 20)^n}{n!}.

Learn more about probability here

brainly.com/question/24756209

#SPJ4

You might be interested in
Need help with this problem please
MrMuchimi
I think she bought 23 feet
8 0
3 years ago
There are 10 less trumpet and saxophone players number of saxophone players three times the number of trumpet players how many t
Mrrafil [7]
Let a be the number of trumpet players
Let b be the number of saxophone players
---------------------
(1) a = b-10
(2) b =3a
----------------
Substitute
(2) into (1)
(1) a =3a-10
(1) 2a =10 

 (1) a = 5and
(2) b = 3(5)(2)
b =  15
------------------
There are 5 trumpet players and 15 saxophone player
5 0
3 years ago
If the pool is 3600 ft and cost 0.75 per square foot what is the cost
ikadub [295]
Hi,
side=3600 foot
area=side*side
area=3600*3600
area=129600<span>0</span>0 square foot
cost=area*rate
cost=12960000*0.75
cost=Rs.(or whichever currency)9720000
Hope this helps you.
5 0
3 years ago
Which expression is equal to (x+2)(-x^2+2x-6)
sveticcg [70]

Answer:

Where are the choices?

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help!<br> Pleaseeee
Mumz [18]
(1/2)x +y = 3 (equation 1)
2x +4y = 12 (equation 2)

((1/2)x +y = 3) x4
= 2x +4y = 12

2x +4y = 12
-
2x +4y = 12
= nothing

answer is B infinitely many solutions as the lines are stacked on top of another.
5 0
2 years ago
Read 2 more answers
Other questions:
  • A submarine starts at the surface of the water and travels to the bottom, a depth of 4000 feet. Graph A shows its distance from
    7·2 answers
  • What is the interquartile range of the data set?
    6·1 answer
  • The mass of the sun is about 2×10expont 30 kilograms how many kilograms are in one metric ton
    6·1 answer
  • Solve x + 3y = 9. 3x – 3y = –13
    11·1 answer
  • What is the slope of segment BC?
    12·2 answers
  • What is the measure of angle A, in degrees?​
    15·1 answer
  • Find the perimeter and simplify your answer
    5·1 answer
  • What is six hundred twenty-nine thousandths written in standard form
    12·1 answer
  • Where do I put the dots on the lines
    8·2 answers
  • 10. Depression. A study published in the Archives of
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!