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Problem 2 Fct) (a) Derive and sketch the failure density function (3 marks) (b) Derive and...
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and...
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and sketch the failure density function (8 marks) b) Derive and sketch the and sketch the reliability function (6 marks) (c) Derive and sketch the hazard rate function (6 marks) (d) Would you recommend a burn in period for this motor, why or why not? (4 marks) (e) What is the probability a new molor will last more than 2 years? (4 marks) Determine the...
3. Given the survival function: S(t) exp(-t7) derive the probability density function and the hazard function...
3. Given the survival function: S(t) exp(-t7) derive the probability density function and the hazard function 4 Derive λ t f (t) S(t using the definition of the hazard function and basic definition of conditional probability. 5. Derive S(t) e-) using the definition of the hazard function. 6. Given the hazard function: derive the survival function and the probability density function 7. Prove that if T' has an arbitrary continuous distribution, the cumulative hazard of T, A(T), has an exponential...
- At The exponential density function in the previous problem: t20 is often used to model...
- At The exponential density function in the previous problem: t20 is often used to model the failure of equipment components. That is, the probability that a particular component will fail within time T is given by: f(t)= le- Pf =ff(odt 0 Reliability is defined as the probability that a component will not fail in time T, i.e. R=1-P, a) what is the expected (average) lifetime of a component in terms of 2 ? b) if an electronic component has...
1. The failure rate function of an item is z ( t ) = t^-1/2. Derive:...
1. The failure rate function of an item is z ( t ) = t^-1/2. Derive: The mean time to failure. 2. A component with time to failure T has failure rate function z ( t ) = kt fort > 0 and k > 0. Determine the probability that a component which is functioning after 200 hours is still functioning after 400 hours, when k = 2.*10^-6 (hours).
(7 marks) 0.07) (3 marks) Find the lot quality level that will be rejected in 85% of the time. (ii) Figure 4(b) shows the sketch diagram for an electric generator. Construct a fuhtee İor the case...
(7 marks) 0.07) (3 marks) Find the lot quality level that will be rejected in 85% of the time. (ii) Figure 4(b) shows the sketch diagram for an electric generator. Construct a fuhtee İor the case that the motor cannot be turned on based on the available information. The following probabilities are given Power source failure 0.010 (b) Switch I failure 0.003 Switch 2 failure -0.004 Switch 3 failure 0.002 Blown fuse-0.002 Motor out 0.030 Wire broken 0.010 All Electric...
For a particular brand of smart phone, the reliability function is R1(t) = 1 for 0 Rr() expt-3] for t> 3, with time t in years. Here, expla] means e a. Sketch RT(t) versus t. Show proper axis l...
For a particular brand of smart phone, the reliability function is R1(t) = 1 for 0 Rr() expt-3] for t> 3, with time t in years. Here, expla] means e a. Sketch RT(t) versus t. Show proper axis labels, scales, and units. b. Express cumulative distribution function (CDF) Fr(t1) mathematically, and sketch it below Rr() to t 3 and 3. the same horizontal scale. Set Fr(t) 0 for t < 0. Show proper axis labels, scales, and units. Express mathematically...
with steps pleas thanks 6. (20 Marks) If joint probability density function (pdliy of Xand is...
with steps pleas thanks
6. (20 Marks) If joint probability density function (pdliy of Xand is dehined S f(x, y) ={Cry a) Find C to have a valid joint density function x+ysi 0, Otherwise b) Find marginal pdfs of X and Y. (20 marks) Assume survival of transplanted hearts has an Exponential distribution with mean of 5 years. If a transplanted heart survives less than 4 years, the transplant is considered failure. Assume heart transplants are independent of each other,...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks]...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks] b) An electronic system contains in components which are connected in series and they i) Describe the meaning of each term in the equation ii) Write down an expression for the unconditional probability P() in terms of iii) Describe the implications omrix)>MYIX). quantities in the above equation. function independently of each other. The length of time for each component until failure follows an exponential...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks]...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks] b) An electronic system contains in components which are connected in series and they i) Describe the meaning of each term in the equation ii) Write down an expression for the unconditional probability P() in terms of iii) Describe the implications omrix)>MYIX). quantities in the above equation. function independently of each other. The length of time for each component until failure follows an exponential...
Course: Mathematical Statistics (Sept 2018 Qualifying Exam) Problem 2. The density function for the random variable,...
Course: Mathematical Statistics (Sept 2018 Qualifying Exam)
Problem 2. The density function for the random variable, T, that denotes the life time of a bulb (in years) is given by: 6 - t f(t) = 12,0<t<6 (1) What is the average life time of bulb? (2) The bulb still works after the 2 years. What is the probability that the blub can last at least another year? (3) If the cost in dollars of replace a blub is given by...
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and sketch the failure density function (8 marks) b) Derive and sketch the and sketch the reliability function (6 marks) (c) Derive and sketch the hazard rate function (6 marks) (d) Would you recommend a burn in period for this motor, why or why not? (4 marks) (e) What is the probability a new molor will last more than 2 years? (4 marks) Determine the...
3. Given the survival function: S(t) exp(-t7) derive the probability density function and the hazard function 4 Derive λ t f (t) S(t using the definition of the hazard function and basic definition of conditional probability. 5. Derive S(t) e-) using the definition of the hazard function. 6. Given the hazard function: derive the survival function and the probability density function 7. Prove that if T' has an arbitrary continuous distribution, the cumulative hazard of T, A(T), has an exponential...
- At The exponential density function in the previous problem: t20 is often used to model the failure of equipment components. That is, the probability that a particular component will fail within time T is given by: f(t)= le- Pf =ff(odt 0 Reliability is defined as the probability that a component will not fail in time T, i.e. R=1-P, a) what is the expected (average) lifetime of a component in terms of 2 ? b) if an electronic component has...
(7 marks) 0.07) (3 marks) Find the lot quality level that will be rejected in 85% of the time. (ii) Figure 4(b) shows the sketch diagram for an electric generator. Construct a fuhtee İor the case that the motor cannot be turned on based on the available information. The following probabilities are given Power source failure 0.010 (b) Switch I failure 0.003 Switch 2 failure -0.004 Switch 3 failure 0.002 Blown fuse-0.002 Motor out 0.030 Wire broken 0.010 All Electric...
For a particular brand of smart phone, the reliability function is R1(t) = 1 for 0 Rr() expt-3] for t> 3, with time t in years. Here, expla] means e a. Sketch RT(t) versus t. Show proper axis labels, scales, and units. b. Express cumulative distribution function (CDF) Fr(t1) mathematically, and sketch it below Rr() to t 3 and 3. the same horizontal scale. Set Fr(t) 0 for t < 0. Show proper axis labels, scales, and units. Express mathematically...
with steps pleas thanks
6. (20 Marks) If joint probability density function (pdliy of Xand is dehined S f(x, y) ={Cry a) Find C to have a valid joint density function x+ysi 0, Otherwise b) Find marginal pdfs of X and Y. (20 marks) Assume survival of transplanted hearts has an Exponential distribution with mean of 5 years. If a transplanted heart survives less than 4 years, the transplant is considered failure. Assume heart transplants are independent of each other,...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks] b) An electronic system contains in components which are connected in series and they i) Describe the meaning of each term in the equation ii) Write down an expression for the unconditional probability P() in terms of iii) Describe the implications omrix)>MYIX). quantities in the above equation. function independently of each other. The length of time for each component until failure follows an exponential...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks] b) An electronic system contains in components which are connected in series and they i) Describe the meaning of each term in the equation ii) Write down an expression for the unconditional probability P() in terms of iii) Describe the implications omrix)>MYIX). quantities in the above equation. function independently of each other. The length of time for each component until failure follows an exponential...
Course: Mathematical Statistics (Sept 2018 Qualifying Exam)
Problem 2. The density function for the random variable, T, that denotes the life time of a bulb (in years) is given by: 6 - t f(t) = 12,0<t<6 (1) What is the average life time of bulb? (2) The bulb still works after the 2 years. What is the probability that the blub can last at least another year? (3) If the cost in dollars of replace a blub is given by...
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