Homework Answers
Add Answer to:
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A...
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) 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...
Let X be the lifetime of a certain type of electronic device (measured in hours). The...
Let X be the lifetime of a certain type of electronic device (measured in hours). The probability density function of X is f(x) =10/x^2 , x > c 0, x ≤ c (a) Find the value of c that makes f(x) a legitimate pdf of X. (b) Compute P(X < 20).
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
An electrical firm manufactures a certain type of LED light bulb and claims that the average bulb lifetime is at least 800 hours
An electrical firm manufactures a certain type of LED light bulb and claims that the average bulb lifetime is at least 800 hours. To test this, a random sample of 60 bulbs is taken. The average life of the sample is found to be 788 hours with a standard deviation of 40 hours.(a) At a level of 0.05 significance, is there compelling evidence to doubt the comp any's claim? Be sure to state the appropriate hypotheses, and specify the rejection...
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of...
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....
4. Let X and Y be random variables of the continuous type having the joint pdf...
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
The lifetime, in years, of a certain type of pump is a random variable with probability...
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (x+1) 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find the...
3 Minimum of IID exponentials Let Z1, ..., Zn be IID exponential random variables with mean...
3 Minimum of IID exponentials Let Z1, ..., Zn be IID exponential random variables with mean 8. That is, each Z has a PDF given by: f(3) = exp(-z/B], where 2 and 3 are positive. x f(x) dx Derive the probability density function for min(Z......) (.e., the minimum of random variables 21,..., 2n). You should find that the probability density function for min(Z1,..., Zn) is that of an expo nential random variable. What is the mean of min(21,..., 2..)?
There are two fuses in an electrical device. Let X denote the lifetime of the first...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is f(x,y) = (x? + 2 + 2) 0<x< 1, 0 < y < 2 a. What is the probability that both fuses last at most 4 months? b. What is the probability that the first fuse lasts less than...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (x+1) 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find the...
3 Minimum of IID exponentials Let Z1, ..., Zn be IID exponential random variables with mean 8. That is, each Z has a PDF given by: f(3) = exp(-z/B], where 2 and 3 are positive. x f(x) dx Derive the probability density function for min(Z......) (.e., the minimum of random variables 21,..., 2n). You should find that the probability density function for min(Z1,..., Zn) is that of an expo nential random variable. What is the mean of min(21,..., 2..)?
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is f(x,y) = (x? + 2 + 2) 0<x< 1, 0 < y < 2 a. What is the probability that both fuses last at most 4 months? b. What is the probability that the first fuse lasts less than...
Most questions answered within 3 hours.
-
Required information
[The following information applies to the questions
displayed below.]
In 2019, Alliant Corporation acquired...
asked 15 minutes ago -
How much must I invest today if I want to withdraw 1/3 of my
original investment...
asked 2 hours ago -
What is meant by a “term premium”?
What can explain such a premium? Is it a...
asked 4 hours ago -
23. Which molecule has only covalent bonds? A. CO2 B. Al2O3 C.
Mg3N2
24. The octet...
asked 4 hours ago -
the
total pressure for a mixture of N2O4 and NO2 is 2.20 atm. If Kp=
7.10...
asked 4 hours ago -
Delaware Corp. prepared a master budget that included $22,385
for direct materials, $28,600 for direct labor,...
asked 4 hours ago -
For pesticide HCB (hexachlorobenzene), its logarithmic partition
coefficient log Kow is 5.6. What would be the...
asked 4 hours ago -
A chemist requires 0.422 mil Na2CO3 for a reaction. How many
grams does this correspond to?
asked 4 hours ago -
If the vapor pressure of carvone is approximately 9.4 torr at 99
°C, approximately how much...
asked 4 hours ago -
A juice bottling company is carrying out a test at 10%
significance that the mean population...
asked 5 hours ago -
What is the reflectivity (in percent) needed to keep water at a
temperature near its freezing...
asked 5 hours ago -
Suppose that the average surface temperature of Earth is 300K.
Assume this is uniform over its...
asked 5 hours ago