(a) A lamp has two bulbs of a type with an average lifetime of 1300 hours.
(a) A lamp has two bulbs of a type with an average lifetime of 1300 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean u = 1300, find the probability that both of the lamp's bulbs fail within 1500 hours. (Round your answer to four decimal places.)
(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1500 hours. (Round your answer to four decimal places.)
Homework Answers
Add Answer to:
(a) A lamp has two bulbs of a type with an average lifetime of 1300 hours.
A type of lightbulb is labeled as having an average lifetime of 1000 hours.
(a)A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean μ = 1000. (i) Use this model to find the probability that a bulb fails within the first 500 hours (Round your answer to three decimal places.) (ii) Use this model to find the probability that a bulb bums for more than 700 hours. (b) What is the median lifetime of...
A homeowner buys a package of four light bulbs, each of which has an average lifetime...
A homeowner buys a package of four light bulbs, each of which has an average lifetime of 1000 hours. The homeowner, being an organized gentleman, places one of the bulbs from the package in a lamp, and the instant it burns out, replaces it with another. He continues this process until all four bulbs have burned out. For the first light bulb, what kind of random variable is X if X models the amount of time before it burns out?
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A...
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf fa(ylx) of Y given Xx. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B...
The life of light bulbs is distributed normally. The variance of the lifetime is 400400 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 400400 and the mean lifetime of a bulb is 600600 hours. Find the probability of a bulb lasting for at most 633633 hours. Round your answer to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 527 hours. Round your answer to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 570 hours. Find the probability of a bulb lasting for between 532 and 599 hours. Round your answer to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 400 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 400 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for between 518 and 552 hours. Round your answer to four decimal places.
Two light bulbs, have exponential lifetime where expected lifetime for bulb A is 500 hours and ex...
Two light bulbs, have exponential lifetime where expected lifetime for bulb A is 500 hours and expected lifetime for bulb B is 200 hours. a) What is the expected time until bulb A or bulb B malfunctions ? b) What is the probability that bulb A malfunctions before bulb B ?
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15...
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 580 hours. Find the probability of a bulb lasting for at least 590 hours. Round your answer to four decimal places.
.The life of light bulbs is distributed normally. The standard deviation of the lifetime is 20...
.The life of light bulbs is distributed normally. The standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 570 hours. Find the probability of a bulb lasting for at least 597 hours. Round your answer to four decimal places.
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf fa(ylx) of Y given Xx. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B...
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 570 hours. Find the probability of a bulb lasting for between 532 and 599 hours. Round your answer to four decimal places.
Most questions answered within 3 hours.
-
Question 1
At the end of Year 6,
South Co.'s tax department estimates that they will...
asked 5 minutes ago -
Need help in drawing out a map pathway of pentose phosphate
pathway and pyruvate dehydrogenase/citric acid...
asked 3 minutes ago -
Use standard enthalpies of formation to determine
ΔHorxn for:
1. 3NO2(g) + H2O(l) → 2HNO3(aq)
+...
asked 10 minutes ago -
Abigail Adams was hired as an associate professor of economics
at Heartland University. She was the...
asked 12 minutes ago -
consider the overall reaction: AB(g) + CB(g) ⟶ A(g) + CB2(g)
A proposed mechanism for this...
asked 19 minutes ago -
In fruit flies, assume bright red eyes (r) and curly wing (w)
are encoded by two...
asked 34 minutes ago -
Consider the compounds represented by the following names:
Compound A: 2,3-dimethylpentane Compound B: 3,4-dimethyl-3-pentene
Compound C:...
asked 39 minutes ago -
C3H8 + 5O2 produces 3CO2 + 4
H2O
How many grams of CO2 are
produced by...
asked 39 minutes ago -
Select a target behavior from your list of potential target
behaviors. State your target behavior in...
asked 54 minutes ago -
Guns make a unique marking on the bullets they fire and their
shell casings. These markings...
asked 57 minutes ago -
Bourque Enterprises is considering a new project. The project
will generate sales of $1.5 million, $2.2...
asked 1 hour ago -
data structures c++
please implement the QuickSort algorithm as a C++ function. Use
it to sort...
asked 1 hour ago