Question

The working life (in years) of a certain type of machines is an exponential random variable...

The working life (in years) of a certain type of machines is an exponential random variable with parameter λ, which depends on the quality of its chip. Suppose that the quality of chips are random in a sense that λ is uniformly distributed between [0.5, 1].

1.Find the expected working life of a machine.

2.Find the variance of the working time of a machine.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given an exponential random variable X with parameter θ and θ is uniformly distributed on the...
Given an exponential random variable X with parameter θ and θ is uniformly distributed on the interval (2,4). Solve for the expected value and variance of X.
Let X be an exponential random variable with parameter λ > 0. Find the probabilities P(...
Let X be an exponential random variable with parameter λ > 0. Find the probabilities P( X > 2/ λ ) and P(| X − 1 /λ | < 2/ λ) .
Let X be a random variable with an exponential distribution and suppose P(X > 1.5) =...
Let X be a random variable with an exponential distribution and suppose P(X > 1.5) = .0123 What is the value of λ? What are the expected value and variance? What is P(X < 1)?
Suppose that a certain system contains three components that function independently of each other and are...
Suppose that a certain system contains three components that function independently of each other and are connected in series, so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component, X1, measured in hours, has an exponential distribution with parameter λ = 0.01; the length of life of the second component, X2, has an exponential distribution with parameter λ = 0.03; and the length of life of the...
let X be a random variable that denotes the life (or time to failure) in hours...
let X be a random variable that denotes the life (or time to failure) in hours of a certain electronic device. Its probability density function is given by f(x){ 0.1 e−0.1x, x > 0 , 0 , elsewhere (a) What is the mean lifetime of this type of device? (b) Find the variance of the lifetime of this device. (c) Find the expected value of X2 − 20X + 100.
The battery life of a certain fire alarm, denoted by X, follows an exponential distribution with...
The battery life of a certain fire alarm, denoted by X, follows an exponential distribution with mean 3 hours. Suppose we take a random sample of 36 fire alarms. Answer the following questions. A. Find the probability that a single fire alarm will operate for at least 6 hours. B. Find the probability that the total battery lifetime based on the 36 fire alarms will be more than 126 hours. C. If the sample mean was 3.5, find a 95%...
A random sample of n = 15 heat pumps of a certain type yielded the following...
A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0     1.5     6.0     1.7 5.2 0.4     1.0     5.3 15.7 0.5 4.8 0.9     12.2     5.3 0.6 (a) Assume that the lifetime distribution is exponential and use an argument parallel to that of this example to obtain a 95% CI for expected (true average) lifetime. (Round your answers to two decimal places.) ________ and _________ years (b.) What is a 95%...
Suppose a chandelier has 2019 bulbs, each has independent random lifetimes that is uniformly distributed on...
Suppose a chandelier has 2019 bulbs, each has independent random lifetimes that is uniformly distributed on an interval [0,β] with the same variance as an exp(1/4) variable. (You have to figureout the value of β.) Find the expected time until 2001 bulbs have burned out.
The lifespan of a virus depends on the type of RNA it carries. There are two...
The lifespan of a virus depends on the type of RNA it carries. There are two types of RNA that a virus can randomly carry. The probability that a virus carries type 1 RNA is 0.4 and the probability it carries type 2 RNA is 0.6. For a given type of RNA, the lifespan of a virus is random and can be characterized as exponential. The average amount of time for the virus to exhibit no bio-activity is about 4...
The life of a particular type of fluorescent lamp is exponentially distributed with expectation 1 ....
The life of a particular type of fluorescent lamp is exponentially distributed with expectation 1 . 6 years. Let T be the life of a random fluorescent lamp. Assume that the lifetimes of different fluorescent lamps are independent. a) Show that P ( T> 1) = 0 . 535. Find P ( T < 1 . 6). In a room, 8 fluorescent lamps of the type are installed.Find the probability that at least 6 of these fluorescent lamps still work...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT