linear Alg-2 jobs
strength
Corrections.docx
NOTE : 3(B) ,3(C) ,4(B),4(C),5(A),5(B) ARE WRONG . AS A PROOF I PASTED THERE
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Question 1: (3 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
Suppose that the lifetime, T, for a certain type of disk drive follows an exponential distribution.
(a) If it is given that 6% of drives fail within 2 years, find the parameter λ for the exponential distribution. _____5.5466_____
(b) Find E(T). _____5.5466_____
(c) Calculate the probability that the lifetime T for a randomly chosen disk drive exceeds 0.9 years. _____3.3070*10^-7_____
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Question 2: (2 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
Suppose the discrete random variable X has the following probability distribution.
(a) Find E(X). ____8.75______ Explanation:
(b) Find var(X). ____11.0875______
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Question 3: (3 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
In a certain workshop, the total cost, C for servicing a car is
C=X+80Y
where X is the cost of parts and Y is the time (in hours) taken to perform the service. Suppose, for a randomly chosen car, that
X∼N(120,202)
and
Y∼N(2.6,0.52) independently.
(a) Find E(C). _____328_____
(b) Find var(C). _____206.16_____
(c) Find the probability that the total cost of service, for a randomly chosen car, will be no more than $350.00.
Probability =
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Question 4: (3 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
Suppose that the diameters of particles in a sediment are distributed uniformly between 0.5 and 2.1 mm. Let D be the diameter of randomly chosen particle.
(a) Find E(D). ______1.3______
(b) Find the standard deviation sd(D). _____0_____ 0 since uniformly distributed
(c) Find the proportion of particles with diameters between 0.6 and 0.9 mm. ____0.0900______
Probability =
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Question 5: (2 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
Let X and Y be independent random variables with variances 7 and 1 respectively and let Z=X+Y.
(a) What is the value of cov(X,Z)? ______2.6457______
(b) What is the value of the correlation coefficient ρX,Z? _____0.3780_____
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