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
umka2103 [35]
3 years ago
13

Thetime(inhours)requiredtorepairamachineis an exponentially distributed random variable with parameter λ = 1 . What is 2 (a) the

probability that a repair time exceeds 2 hours? (b) the conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours?
Mathematics
1 answer:
mihalych1998 [28]3 years ago
4 0

Answer:

a) 0.1353

b) 0.3679

Step-by-step explanation:

Let's start by defining the random variable T.

T : ''The time (in hours) required to repair a machine''

T ~ exp (λ)

T ~ exp (1)

The probability density function for the exponential distribution is

(In the equation I replaced λ = L)

f(x)=Le^{-Lx}

With L > 0 and x ≥ 0

In this exercise λ = 1 ⇒

f(x)=e^{-x}

For a)

P(T>2)

P(T>2)=1-P(T\leq 2)

P(T>2)=1-\int\limits^2_0 {e^{-x} } \, dx

P(T>2)=1-(-e^{-2}+1)

P(T>2)=e^{-2}=0.1353

For b)

P(T\geq 10/T>9)

The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur

P(T\geq 10/T>9)=P(T\geq 1)

P(T\geq 1)=1-P(T

P(T\geq 1)=1-(-e^{-1}+1)=e^{-1}=0.3679

You might be interested in
I know the answer is A....but why?
katrin2010 [14]

Answer:a

Step-by-step explanation:

throughout the table it is presented that the answer, A, is correct becuase within the percentages is is obvious that a is correct.

6 0
3 years ago
Read 2 more answers
You throw a softball into the air with an initial upward velocity of 38 ft/s and an initial height of 5 feet. Use the vertical m
ddd [48]
I’m so sorry I need points but I’m gonna manifest that someone smarter will see this and answer
7 0
3 years ago
Whoever answers this NOW will get brainliest
gavmur [86]

Answer:

I think is -x + 105/42y

Step-by-step explanation:

2(3/10)x - 5/7y - 4(5/6)y - 2(4/5)x

6/10x - 5/7y - 20/6y - 8/5x

6/10x - 8/5x - 5/7y - 20/6y

6-16/10x - 35+140/42y

-10/10x + 105/42y

-x + 105/42y

5 0
3 years ago
Pls help me answer the question and if you don't know, pls don't answer. thank you!
Damm [24]
The answer is 162in2 to its orbit
6 0
3 years ago
Cos^2 2x−cos^2 6x=sin4x sin8x<br> please help me prove it
Olin [163]
Cos² 2x = (1+cos 4x )/2
cos² 6x  = (1+cos 12x)/2
subtract to get  1/2 (cos 4x - cos 12x )   
=  1/2 (2 sin  4x sin 8x )       as cos A - cos B =  2 [ sin (A+B)/2  sin (A-B)/2 ]
so the answer
4 0
3 years ago
Other questions:
  • What are the x-intercept and the y-intercept of the graph of y=−3x−18 ? Enter your answers in the boxes.
    9·2 answers
  • What is the slope of this line? <br><br> Enter your answer in the box.
    14·2 answers
  • WILL GIVE BRAINLIEST!!!!!! PLEASE HELP ME!!! 12 POINTS!!!!!
    8·1 answer
  • In this polygon, which angle is an interior angle?
    14·2 answers
  • Colton and his dad bought a gallon of paint that costs $13 . They also bought 2 brushes that cost $9 each. What was the total co
    7·2 answers
  • Question: What is the slope of the line?
    7·1 answer
  • Need help answering a question text me now
    6·1 answer
  • What the answer please​
    6·2 answers
  • Estimate 349.6-112.8 to find the correct answer
    5·1 answer
  • -7x/6=-2x/1<br> Solve for X
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!