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2) The lifetime in years of a certain type of electronic component has a probability density...
2. A certain type of electronic component has a lifetime X (in hours) with probability density...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
The lifetime, in years, of a certain type of pump is a random variable with probability...
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (x+1) 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find the...
1) A mining company has a test that can identify coal in a sample. We know...
1) A mining company has a test that can identify coal in a sample. We know that 93% of a particular area that the mining company has leased contains no coal. Given a sample that has no coal is tested, containing coal (given it actually does contain coal) 4.5% of the time. a) State each event. b) Write out the probabilities for this scenario using the probability notation taught in lectures and workshops c) Find the probability of finding coal...
x 20 The lifetime, in years, of a certain type of pump is a random variable...
x 20 The lifetime, in years, of a certain type of pump is a random variable with probability density function 3 (x+1)+ 0 True (Note: “True" means “Otherwise” or “Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find...
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by That is, Y has a gamma distribution with parameters α = 2 and θ. Let denote the MLE of θ. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of θ. b Find E() and V(). c Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What...
The probability density function of X, the lifetime of a certain type of electronic device (measured...
The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by fX(x) = ( C/x^2 x>5 0 x<5 where C>0 is a constant which needs to be determined. (i) What is the probability that the device’s lifetime is 10 hours? (ii) Find the 25%th quantile of X? (iii) If the device lifetime is X, then its total electricity cost equals . What is the expected total electricity cost of the...
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 No. 4 / 10 pts. Given The lifetime, in years, of a certain type of...
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....
Problem No. 6.4 / 10 pes. The lifetime, in years of a certain type of pump...
Problem No. 6.4 / 10 pes. The lifetime, in years of a certain type of pump is a random variable with probability density function .x20 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the...
RANU 10 pts. Problem No. 6.4 The lifetime, in years, of a certain type of pump...
RANU 10 pts. Problem No. 6.4 The lifetime, in years, of a certain type of pump is a random variable with probability density function (x+1)* x20 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (x+1) 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find the...
1) A mining company has a test that can identify coal in a sample. We know that 93% of a particular area that the mining company has leased contains no coal. Given a sample that has no coal is tested, containing coal (given it actually does contain coal) 4.5% of the time. a) State each event. b) Write out the probabilities for this scenario using the probability notation taught in lectures and workshops c) Find the probability of finding coal...
x 20 The lifetime, in years, of a certain type of pump is a random variable with probability density function 3 (x+1)+ 0 True (Note: “True" means “Otherwise” or “Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find...
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 No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....
Problem No. 6.4 / 10 pes. The lifetime, in years of a certain type of pump is a random variable with probability density function .x20 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the...
RANU 10 pts. Problem No. 6.4 The lifetime, in years, of a certain type of pump is a random variable with probability density function (x+1)* x20 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of...
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