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A device runs until either of two components fails, at which time the device stops running. The j...
13. (5 marks) In order for a device to run, two batteries must both be functional....
13. (5 marks) In order for a device to run, two batteries must both be functional. Let X be the lifetime of battery 1, and Y be the lifetime of battery 2, both measured in days. Suppose the joint density of X and Y is given as 0 otherwise If you just turned on the device with these new batteries, what is the expected life of the machine? That is, what the expected time to wait until the first battery...
13. (5 marks) In order for a device to run, two batteries must both be functional....
13. (5 marks) In order for a device to run, two batteries must both be functional. Let X be the lifetime of battery 1, and Y be the lifetime of battery 2, both measured in days. Suppose the joint density of X and Y is given as f(x, y)-po 0 , otherwise If you just turned on the device with these new batteries, what is the expected life of the machine? That is, what the expected time to wait until...
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...
Two electronic components of a missile system work in harmony for the success of the total...
Two electronic components of a missile system work in harmony for the success of the total system. Let X and Y denote the life in hours of the two components. The joint density of X and Y is −y(1+x) ye , x, y ≥ 0, f(x, y) = 0, elsewhere. (a) Give the marginal density functions for both random variables. (b) What is the probability that the lives of both components will exceed 2 hours?
I can do the first part of the question 1a, could someone show me step by...
I can do the first part of the question 1a, could
someone show me step by step how to do do 1b?
) Y.Ya..., Y, form a random sample from a probability distribution with cumu- lative distribution function Fy (u) and probability density function fr(u). Let Write the cumulative distribution function for Ya) in terms of Fy(y) and hence show that the probability density function for Yy is fy(1)(y) = n(1-Fr (v))"-ify(y). [8 marks] (b) An engineering system consists of...
®, X and Y are two random variables denoting the proportions of time during which employees...
®, X and Y are two random variables denoting the proportions of time during which employees I and II work on a weekday respectively. The joint density of X and Y is x+y, İf 0 < x < 1, 0<y<1, 0, esewhere. (a) Find P(XY Hint: Definition of conditional probability: P(AB)- P(AnB)/P(B) (b) Find P(XY)
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...
. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetim...
. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetimes of the two components observed at discrete time units (e.g.,every hour). Assume that the joint PMF of X and Y is px.y(x, y) = p (1 - p)*+-2 if x, y e N, and px.Y(x, y) 0 otherwise, where O <p< l. Use the FPF for two discrete random variables to determine the probability that one of the components lasts...
5. The total time, measured in units of 100 hours, that a teenager runs her hair...
5. The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function (r, f(0) = {2-r, 10, if 0 < x <1, if 1 <<2, elsewhere. Evaluate the mean of the random variable Y = 60X2 + 39X, where Y is equal to the number of kilowatt hours expended annually.
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...
13. (5 marks) In order for a device to run, two batteries must both be functional. Let X be the lifetime of battery 1, and Y be the lifetime of battery 2, both measured in days. Suppose the joint density of X and Y is given as 0 otherwise If you just turned on the device with these new batteries, what is the expected life of the machine? That is, what the expected time to wait until the first battery...
13. (5 marks) In order for a device to run, two batteries must both be functional. Let X be the lifetime of battery 1, and Y be the lifetime of battery 2, both measured in days. Suppose the joint density of X and Y is given as f(x, y)-po 0 , otherwise If you just turned on the device with these new batteries, what is the expected life of the machine? That is, what the expected time to wait until...
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...
I can do the first part of the question 1a, could
someone show me step by step how to do do 1b?
) Y.Ya..., Y, form a random sample from a probability distribution with cumu- lative distribution function Fy (u) and probability density function fr(u). Let Write the cumulative distribution function for Ya) in terms of Fy(y) and hence show that the probability density function for Yy is fy(1)(y) = n(1-Fr (v))"-ify(y). [8 marks] (b) An engineering system consists of...
®, X and Y are two random variables denoting the proportions of time during which employees I and II work on a weekday respectively. The joint density of X and Y is x+y, İf 0 < x < 1, 0<y<1, 0, esewhere. (a) Find P(XY Hint: Definition of conditional probability: P(AB)- P(AnB)/P(B) (b) Find P(XY)
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...
. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetimes of the two components observed at discrete time units (e.g.,every hour). Assume that the joint PMF of X and Y is px.y(x, y) = p (1 - p)*+-2 if x, y e N, and px.Y(x, y) 0 otherwise, where O <p< l. Use the FPF for two discrete random variables to determine the probability that one of the components lasts...
5. The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function (r, f(0) = {2-r, 10, if 0 < x <1, if 1 <<2, elsewhere. Evaluate the mean of the random variable Y = 60X2 + 39X, where Y is equal to the number of kilowatt hours expended annually.
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...
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