Suppose the time to failure follows an exponential distribution with parameter λ. Based on type II...

Suppose the time to failure follows an exponential distribution with parameter λ. Based on type II censoring determine the likelihood and the maximum likelihood estimator for λ. Assume that n = 3 and the experiment ends after 2 failures.

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orchestra answered 1 year ago

For a random sample of sizenfrom an Exponential distribution with rate parameter λ (so that the...

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A certain type of pump’s time until failure has an exponential distribution with a mean of...

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5) The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours. a) What is the probability that a battery will last more than 14 hours? b) Once a battery is depleted, it is replaced with a new battery of the same type. Assuming independence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours? c) What is the probability that it takes less than...

The exponential distribution with rateλhas meanμ= 1/λ. Thus the method of moments estimator of λ is...

The exponential distribution with rateλhas meanμ= 1/λ. Thus the method of moments estimator of λ is 1/X. Use the following steps to verify that X is unbiased, but 1/X is biased. USING R: a) Generate 10000 samples of size n= 5 from the standard exponential distribution (i.e.λ= 1) using rexp(50000) and arranging the 50000 random numbers in a matrix with 5 rows. b) Use the apply() function to compute the 10000 sample means and store them in the object means....

The exponential distribution with rate λ has mean μ = 1/λ. Thus the method of moments...

The exponential distribution with rate λ has mean μ = 1/λ. Thus the method of moments estimator of λ is 1/X. Use the following steps to verify that X is unbiased, but 1/X is biased. a) Generate 10000 samples of size n = 5 from the standard exponential distribution (i.e. λ = 1) using rexp(50000) and arranging the 50000 random numbers in a matrix with 5 rows. b) Use the apply() function to compute the 10000 sample means and store...

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