Someone claims that the waiting time, in minutes, between hits at a certain website has the exponential distribution with parameter λ = 0.990. Let X be the waiting time until the next hit. 1. If the claim is true, what is P(X ≥ 5)? (Round the final answer to four decimal places.) 2. Based on the answer to P(X ≥ 5), if the claim is true, is five minutes an unusually long time to wait? (Yes or No) 3. If you waited five minutes until the next hit occurred, would you still believe the claim? Explain. (Yes or No)
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Someone claims that the waiting time, in minutes, between hits at a certain website has the exponential distribution with parameter λ = 0.990. Let X be the waiting time until the next hit.
1. If the claim is true, what is P(X ≥ 5)? (Round the final answer to four decimal places.)
2. Based on the answer to P(X ≥ 5), if the claim is true, is five minutes an unusually long time to wait? (Yes or No)
3. If you waited five minutes until the next hit occurred, would you still believe the claim? Explain. (Yes or No)
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- Suppose X has a lognormal distribution with parameters mu = 1.5 and sigma = 0.2 . Find the 33rd percentile?When I go swimming, the distance in meters that I can swim before getting cramp in one of my hands is exponentially distributed with parameter ?=1/313.3λ=1/313.3. What is the probability that, on a random occasion when I go swimming, I swim at least 593.3593.3 meters without getting hand cramp?Give your solution accurate to 4 decimal places.Suppose X1, . . . , Xn ∼ Exponential(λ) is a set of n observations drawn independently from an Exponential distribution.(a) Write out the likelihood function. (b) Write out the log-likelihood function. (c) Find the score function by taking the partial derivative of the log-likelihood function. (d) Set the score function equal to zero and solve for the parameter λ. (e) Take the second partial derivative of the score function. (f) Check to make sure this value is negative to ensure that the log-likelihood function is concave down.