Homework Answers
Add Answer to:
- (a) The failure time is 15 points) opns below PDF years (x) of a component...
5. (15 Points) Let T be a random variable that is the time to failure (in...
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function f(x,A) =e, if >0 10, otherwise. Compute the probability that a given component will fail in 5 years or less.
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function...
The time to failure T of a component has probability density f ( t ) as...
The time to failure T of a component has probability density f (
t ) as shown
(b) Derive the corresponding survivor function R ( t ) .
(c) Derive the corresponding failure rate function z ( t ) , and
make a sketch of z(t)
Note: The f(t) is a valid pdf (so we can obtain c or the height
of the triangle). Information are enough to solve this problem.
f(t) a -b a b Time t Fig. 2.27...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this r...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours.
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y)...
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y) = 27ye-3 y<x<0, y >0. Show that the joint moment generating function(mgf) of X and Y is 27 M(t1, tz) = tı <3, tı + t, <3 (3 - tı) (3 - 7ı - t2) Use the joint mgf to obtain Cov(X,Y). b) Let X1, X2, X3 be independent random variables representing the lifetime of 3 electronic components with the following pdf, where X...
(1)The field test data in respect of 172 components is as given below. In the life-testing...
(1)The field test data in respect of 172 components is as given below. In the life-testing of 100 specimens of a particular device, the number of failures during each time interval of twenty hours is shown in Table below. Estimate and Plot: the hazard function, failure density and reliability function. Time/Hours Failure 0-1000 59 1000-2000 24 2000-3000 3000-4000 4000-5000 5000-6000 29 30 17 13 (1) calculate the reliability of the system shown in the figure below 0.8 5 0.8 0.9...
Problem 7: [8 points) The life X (in years) of a voltage regulator of a car...
Problem 7: [8 points) The life X (in years) of a voltage regulator of a car has pdf f(1) = 33e-($)" for a > 0. (a) Show that this is a valid p.d.f. [1] (b) Derive the c.d.f. F(x) of X [2] (c) Use your answer in (b) to find the probability that the regulator will last at least 7 years? [1] (d) Given that it has lasted at least 7 years, what is the conditional probability that it will...
Problem 7: 8 points) The life X (in years) of a voltage regulator of a car...
Problem 7: 8 points) The life X (in years) of a voltage regulator of a car has pdf f(x) Bane (9)* for x > 0. (a) Show that this is a valid p.d.f. [1] (b) Derive the c.d.f. F(x) of X [2] (C) Use your answer in (b) to find the probability that the regulator will last at least 7 years? [1] (d) Given that it has lasted at least 7 years, what is the conditional probability that it will...
Q1) Consider two events P and Q. a. Write the general formula used to calculate the probability that either event P occu...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
Assignment 3(Chapter 3) To be submitted due to Dec.3 1. Each time a component is tested,...
Assignment 3(Chapter 3) To be submitted due to Dec.3 1. Each time a component is tested, the trial is a success (S) or failure (F). Suppose the component is tested repeatedly until a success occurs on three consecutive trials. Let Y denote the number of trials necessary to achieve this. List all outcomes corresponding to the five smallest possible values of Y, and state which Y value is associated with each one. 3.A mail-order computer business has six telephone lines....
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function f(x,A) =e, if >0 10, otherwise. Compute the probability that a given component will fail in 5 years or less.
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function...
The time to failure T of a component has probability density f (
t ) as shown
(b) Derive the corresponding survivor function R ( t ) .
(c) Derive the corresponding failure rate function z ( t ) , and
make a sketch of z(t)
Note: The f(t) is a valid pdf (so we can obtain c or the height
of the triangle). Information are enough to solve this problem.
f(t) a -b a b Time t Fig. 2.27...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours.
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y) = 27ye-3 y<x<0, y >0. Show that the joint moment generating function(mgf) of X and Y is 27 M(t1, tz) = tı <3, tı + t, <3 (3 - tı) (3 - 7ı - t2) Use the joint mgf to obtain Cov(X,Y). b) Let X1, X2, X3 be independent random variables representing the lifetime of 3 electronic components with the following pdf, where X...
(1)The field test data in respect of 172 components is as given below. In the life-testing of 100 specimens of a particular device, the number of failures during each time interval of twenty hours is shown in Table below. Estimate and Plot: the hazard function, failure density and reliability function. Time/Hours Failure 0-1000 59 1000-2000 24 2000-3000 3000-4000 4000-5000 5000-6000 29 30 17 13 (1) calculate the reliability of the system shown in the figure below 0.8 5 0.8 0.9...
Problem 7: [8 points) The life X (in years) of a voltage regulator of a car has pdf f(1) = 33e-($)" for a > 0. (a) Show that this is a valid p.d.f. [1] (b) Derive the c.d.f. F(x) of X [2] (c) Use your answer in (b) to find the probability that the regulator will last at least 7 years? [1] (d) Given that it has lasted at least 7 years, what is the conditional probability that it will...
Problem 7: 8 points) The life X (in years) of a voltage regulator of a car has pdf f(x) Bane (9)* for x > 0. (a) Show that this is a valid p.d.f. [1] (b) Derive the c.d.f. F(x) of X [2] (C) Use your answer in (b) to find the probability that the regulator will last at least 7 years? [1] (d) Given that it has lasted at least 7 years, what is the conditional probability that it will...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
Assignment 3(Chapter 3) To be submitted due to Dec.3 1. Each time a component is tested, the trial is a success (S) or failure (F). Suppose the component is tested repeatedly until a success occurs on three consecutive trials. Let Y denote the number of trials necessary to achieve this. List all outcomes corresponding to the five smallest possible values of Y, and state which Y value is associated with each one. 3.A mail-order computer business has six telephone lines....
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago