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
MrRissso [65]
3 years ago
15

The number of years a radio functions is exponentially distributed with parameter λ = 1 8 . If Jones buys a used radio, what is

the probability that it will be working after an additional 8 years?
Mathematics
1 answer:
blsea [12.9K]3 years ago
8 0

Answer:

P(X>8)=e^{-1}

Step-by-step explanation:

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

P(X=x)=\lambda e^{-\lambda x}, x>0

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

X \sim Exp(\lambda=\frac{1}{8})

We can assume that the random variable t represent the number of years that the radio is already here. So the interest is find this probability:

P(X>8|X>t)

We have an important property on the exponential distribution called "Memoryless" property and says this:

P(X>a+t| X>t)=P(X>a)

Where a represent a shift and t the time of interest.

On this case then P(X>8|X>t)=P(X>8+t|X>t)=P(X>8)

We can use the definition of the density function and find this probability:

P(X>8)=\int_{8}^{\infty} \frac{1}{8}e^{-\frac{1}{8}x}dx

=\frac{1}{8} \int_{8}^{\infty} e^{-\frac{1}{8}x}dx

=[lim_{x\to\infty} (-e^{-\frac{1}{8}x})+e^{-1}]=0+e^{-1}=e^{-1}

You might be interested in
PlEaSe HeLp Me !!!!!!!!!!!!!!!!!!!!!!!!!!!!
goblinko [34]

Answer:

I think its A or D

Step-by-step explanation:

1/18 SORRY IF IM WRONG

please mark brainliest

4 0
3 years ago
Read 2 more answers
PLZ HELP! <br> WIL MARK AS BEST ANSWER
prohojiy [21]
There are  12 units in between. You have to remember the number line is in twos. So, when you count the units in between, you have to remember to count in twos. Another way to figure it out is you can count the number of lines above the numbers or plots and multiply times two to find how many units are in between. Again, multiplying it times two is necessary in this equation because it is in units of two. 

So, there are 12 units in between. 
I really hope this helps and I know how I worded it is kind of confusing, but hopefully you understand. If you have any question feel free to ask. Have an awesome day:)
3 0
3 years ago
Write the rational number -1, in the form , where a and b are<br> integers.
iogann1982 [59]

Answer:

2nd option

Step-by-step explanation:

- 5 = \frac{-5}{1} ← in the form \frac{a}{b}

3 0
3 years ago
I will love you forever if someone can help me with this
g100num [7]
It should be B. right angle and C. complementary angles
8 0
3 years ago
Answer correctly please !!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
valina [46]

Answer:

74º

Step-by-step explanation:

  • Ray TV bisects ∠RTS, so ∠RTV=∠STV=(16x-6)º
  • We also know that ∠RTS=(26x+18)º
  • So, (16x-6)º+(16x-6)º=(26x+18)º
  • We don't need parenthesis, 16x-6+16x-6=26x+18
  • Combine like terms, 32x-12=26x+18
  • Add, 32x=26x+30
  • Subtract, 6x=30
  • Divide, x=5
  • ∠RTV now is [16(5)-6]º=(80-6)º=74º
8 0
3 years ago
Other questions:
  • Which shows the following expression using positive exponents?
    10·2 answers
  • Explain the difference of independent and dependent events.
    11·2 answers
  • Whats 1+1 because im having trouble
    13·2 answers
  • A cell phone company orders 600 new phones from a manufacturer. If the probability of a phone being defective is 3.5%, predict h
    6·1 answer
  • If point A is reflected across the y-axis, which pair of coordinates represents the reflection?
    14·1 answer
  • Becky has 4 quarters. Becky's mom gives her 3 more. Becky spends 2 of them on candy. How many quarters does Becky have left?
    13·1 answer
  • A machine can produce 6 yards of fabric in 2 minutes. How much fabric can the machine can produce in 1 hour
    10·1 answer
  • Solve for x if a≠0, a≠3:<br> 3-a/x-a=1/a<br> (a picture will be provided as well)
    13·1 answer
  • Help me with the image i have posted
    11·1 answer
  • Can some body help me with this
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!