&A Library 4.(i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experimentsbased on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the,a) Probability that the average time taken by brand A (?'?) is higher than average time taken by B brand (?'B) is at least 1.0 hour.b) Probability that ?'A will deviate from ?'? by at least 45 minutes.c) How would your answer change if the underlying distribution was not normal? ii) Find a maximum likelihood estimator of μ for a random sample of X1, X2, ….., Xn taken from a Poisson distribution. Clearly write all the steps.
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4.(i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experimentsbased on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the,a) Probability that the average time taken by brand A (?'?) is higher than average time taken by B brand (?'B) is at least 1.0 hour.b) Probability that ?'A will deviate from ?'? by at least 45 minutes.c) How would your answer change if the underlying distribution was not normal? ii) Find a maximum likelihood estimator of μ for a random sample of X1, X2, ….., Xn taken from a Poisson distribution. Clearly write all the steps.
4.(i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experimentsbased on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the,a) Probability that the average time taken by brand A (?'?) is higher than average time taken by B brand (?'B) is at least 1.0 hour.b) Probability that ?'A will deviate from ?'? by at least 45 minutes.c) How would your answer change if the underlying distribution was not normal? ii) Find a maximum likelihood estimator of μ for a random sample of X1, X2, ….., Xn taken from a Poisson distribution. Clearly write all the steps.
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4.(i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to
be formed from water in the freezer was compared. Two independent experiments
based on 15 refrigerators of each brand were performed and time taken in formation of
ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour.
Assuming normal distribution and mean time for both brands is equal to 20 hours, find
the,
a) Probability that the average time taken by brand A (X'A) is higher than average
time taken by B brand (X'B) is at least 1.0 hour.
b) Probability that X'A will deviate from X'B by at least 45 minutes.
c) How would your answer change if the underlying distribution was not
normal?
ii) Find a maximum likelihood estimator of μ for a random sample of X1, X2, ….., Xn
taken from a Poisson distribution. Clearly write all the steps.
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