Machine “A” has 3 components with independent exponential lifetimes (means= 2, 3 & 5 years). ...
Machine “A” has 3 components with independent exponential lifetimes (means= 2, 3 & 5 years). The machine functions if & only if all 3components function. Machine “B” has 2 components with independent exponential lifetimes (means= 5 & 7years). This machine operates if& only if both components function. Determine the probability that, in machine A, the component with the lowest expected lifetime outlasts both of the other components.
(a) 0.1482. (b) 0.1696. (c) 0.2134. (d) 0.2387. (e) 0.2516
Homework Answers
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Machine “A” has 3 components with independent exponential lifetimes (means= 2, 3 & 5 years). ...
Please do #13 10 answer is D 11 answer is A 12 answer is A Please do #13 The options for # 13 is ...
Please do #13
10 answer is D
11 answer is A
12 answer is A
Please do #13 The options for # 13 is
a) .1482
b) .1696
c) .2134
d) .2387
e) .2516
Thank you
10) Machine "A" has 3 components with independent exponential lifetimes means2, 3 & 5 years). The machine functions if & only if all 3 components function. Determine the probability that the machine functions for more than 5 years, given that it has functioned for...
Q. 2 (Gamma and exponential, 30 pts). A parallel system consists of two components with independent...
Q. 2 (Gamma and exponential, 30 pts). A parallel system consists of two components with independent lifetimes. The lifetime Ly of the first component is memoryless: it has the exponential distribution with parameter 1. On the other hand, based on statistical analyses, it is found out that the lifetime L2 of the second component has two independent phases each of which has the same characteristics as L). Therefore, it is assumed that L2 has the gamma distribution with shape index...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and...
Two components of a minicomputer have the following
joint pdf for their useful lifetimes X and Y:
f (x, y) 5 5xe2x(11y) x $ 0 and y $ 0
0 otherwise
a. What is the probability that the lifetime X of the first
component exceeds 3?
b. What are the marginal pdf’s of X and Y? Are the two
lifetimes independent? Explain.
c. What is the probability that the lifetime of at least
one component exceeds 3?
12. Two components...
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of ea...
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of each component follows an exponential distribution with a mean lifetime of 2 years. Determine the probability the machine is still operating after 1.5 years. Suppose the machine in the previous problem requires all three of the components to operate. If the lifetime of each component follows...
Consider a system consisting of three components as pictured. The system will continue to function as...
Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi's are independent of one another and each X, has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to...
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x...
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x y) for 0<50-y < 50 and zero elsewhere a. What is the probability that both components are functioning 20 months from now. b. What is the probability the component with life time X would fail 3 months before the other one? c. Compute the covariance of X, Y d. Compute the expected life of the machine e. What is probability that the two components...
ALL OF QUESTION 3 Question 3: Two components in a personal computer system have lifetimes (in...
ALL OF QUESTION 3
Question 3: Two components in a personal computer system have lifetimes (in years) that are distributed with a joint probability density function given by fx.Y(,y e-#(1+v), 0 < r,0 y, 0, otherwise (a) (3 marks). Find fx(x) (b) (3 marks). Find fy(y) (c) (3 marks). Find the probability that the lifetime of at least one com ponent exceeds 2 years. Question 4
Question 3: Two components in a personal computer system have lifetimes (in years) that...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently....
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: FY 1 xe A1 + + x2 0 and v2 0 1 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe X(1+y)dy = e X for x 2 0 dx = 1 (1 + vi for y xe X(1+y)dx...
2. (10pt) The initial cost of a machine is 3. The lifetime of the machine has an exponential dist...
2. (10pt) The initial cost of a machine is 3. The lifetime of the machine has an exponential distribution with a mean of 3 years. The manufacturer is considering offering the following warranty. - if the machine fails within 1 year, the full purchase price is refunded. if the machine fails after 1 year but before 2 years, 3/4 of the purchase price is refunded. price is refunded, an
Please do #13
10 answer is D
11 answer is A
12 answer is A
Please do #13 The options for # 13 is
a) .1482
b) .1696
c) .2134
d) .2387
e) .2516
Thank you
10) Machine "A" has 3 components with independent exponential lifetimes means2, 3 & 5 years). The machine functions if & only if all 3 components function. Determine the probability that the machine functions for more than 5 years, given that it has functioned for...
Q. 2 (Gamma and exponential, 30 pts). A parallel system consists of two components with independent lifetimes. The lifetime Ly of the first component is memoryless: it has the exponential distribution with parameter 1. On the other hand, based on statistical analyses, it is found out that the lifetime L2 of the second component has two independent phases each of which has the same characteristics as L). Therefore, it is assumed that L2 has the gamma distribution with shape index...
Two components of a minicomputer have the following
joint pdf for their useful lifetimes X and Y:
f (x, y) 5 5xe2x(11y) x $ 0 and y $ 0
0 otherwise
a. What is the probability that the lifetime X of the first
component exceeds 3?
b. What are the marginal pdf’s of X and Y? Are the two
lifetimes independent? Explain.
c. What is the probability that the lifetime of at least
one component exceeds 3?
12. Two components...
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of each component follows an exponential distribution with a mean lifetime of 2 years. Determine the probability the machine is still operating after 1.5 years. Suppose the machine in the previous problem requires all three of the components to operate. If the lifetime of each component follows...
Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi's are independent of one another and each X, has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to...
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x y) for 0<50-y < 50 and zero elsewhere a. What is the probability that both components are functioning 20 months from now. b. What is the probability the component with life time X would fail 3 months before the other one? c. Compute the covariance of X, Y d. Compute the expected life of the machine e. What is probability that the two components...
ALL OF QUESTION 3
Question 3: Two components in a personal computer system have lifetimes (in years) that are distributed with a joint probability density function given by fx.Y(,y e-#(1+v), 0 < r,0 y, 0, otherwise (a) (3 marks). Find fx(x) (b) (3 marks). Find fy(y) (c) (3 marks). Find the probability that the lifetime of at least one com ponent exceeds 2 years. Question 4
Question 3: Two components in a personal computer system have lifetimes (in years) that...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: FY 1 xe A1 + + x2 0 and v2 0 1 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe X(1+y)dy = e X for x 2 0 dx = 1 (1 + vi for y xe X(1+y)dx...
2. (10pt) The initial cost of a machine is 3. The lifetime of the machine has an exponential distribution with a mean of 3 years. The manufacturer is considering offering the following warranty. - if the machine fails within 1 year, the full purchase price is refunded. if the machine fails after 1 year but before 2 years, 3/4 of the purchase price is refunded. price is refunded, an
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