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
Citrus2011 [14]
2 years ago
8

The lifetime of two light bulbs are modeled as independent and exponential random variables X and Y, with parameters lambda and

mu, respectively. The time at which one of those two light bulb first burns out is Z = min (X, Y), what is the PDF of Z?
Mathematics
1 answer:
Scorpion4ik [409]2 years ago
7 0

Answer:

\bf h(x)=max(\lambda,\mu) e^{-max(\lambda,\mu) x}\;(x\geq0)

Step-by-step explanation:

The PDF of X is

\bf f(x)=\lambda e^{-\lambda x}\;(x\geq0)

The PDF of Y is

\bf g(x)=\mu e^{-\mu x}\;(x\geq0)

The means of X and Y are respectively,

\bf \displaystyle\frac{1}{\lambda}\;,\displaystyle\frac{1}{\mu}

so we can see that the larger the parameter, the smaller the mean. Hence the PDF of Z = min(X, Y) is an exponential with the largest parameter of the two.

Therefore, the PDF of Z is

\bf h(x)=max(\lambda,\mu) e^{-max(\lambda,\mu) x}\;(x\geq0)

You might be interested in
An automobile factory,1849 parts are made in 4 hours.what is the average rate at which parts are made per hour?
MAXImum [283]

Answer:

There are 462.25 parts being made per hour

Step-by-step explanation:

<u>Step 1:  Make an equation</u>

An automobile factory, 1849 parts are made in 4 hours.

<em>1849 / 4 = x</em>

<em />

<u>Step 2:  Solve</u>

1849 / 4 = x

<em>462.25 = x</em>

<em />

Answer:  There are 462.25 parts being made per hour

7 0
3 years ago
Read 2 more answers
A car and a girl are 50 miles apart. The girl is traveling at 5 mph and the car is traveling at 45 mph. Will their paths cross?
Temka [501]
It might be about 5 mins
8 0
3 years ago
12 liters equals how much quarts? (1 liter equals about 0.95 quarts) WILL GIVE 20POINTS
Stella [2.4K]

Answer:

12 liters = 12.6803 quarts

Step-by-step explanation:


5 0
3 years ago
Read 2 more answers
Linda bought $87.95 worth of merchandise at an electronics store. She
forsale [732]

Answer:  She paid $66.33

Step-by-step explanation:

The overall amount that you paid for the video game was 87.95. She got 27.79 back as a refund. So you subtract what she paid from her refund. 87.95-27.79 = 60.16.  She also had to pay a fine for the video game. So you add the fine to the amount. 60.16+6.17 = 66.33.

Overall, she paid 66.33.

6 0
2 years ago
Read 2 more answers
Ben saved $66 and spent $30. What percentage of his money did he spend? Round your answer to the nearest whole percent.
emmainna [20.7K]
45%
66/30=45 (repeating), rounds to 45%
8 0
3 years ago
Other questions:
  • What is product of 3 1/3 * 2 1/6 in its simplest form
    10·2 answers
  • Algebra 2 <br><br> Simplify 3+i/2-i
    5·1 answer
  • Solve for p.
    7·2 answers
  • What is the value of n in this equation?(2.4 x 10^3) x (3 x 10^n) = 7.2 x 10^9​
    6·2 answers
  • Meagan is taking piano gymnastics lessons.She has a piano lesson every 7 days and gymnastics lessons.She every 3 days.How obtene
    7·1 answer
  • Whats the answer to number 5 please and thank you? please write down the steps too
    8·2 answers
  • Points (3, 2) and (7, 2) are on the graphs of both quadratic functions f and g. The graph of f opens downward, and the graph of
    9·1 answer
  • What is 10 times 500<br><br> who wants to speak
    13·2 answers
  • Please help with this math problem!! :)
    8·1 answer
  • Solve: 3x2+2x-4=0 <br> Give your answer to 2 decimal places
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!