The number of minutes between successive bus arrivals at NewYork's bus stop is exponentially distributed with...

The number of minutes between successive bus arrivals at NewYork's bus stop is exponentially distributed with unknown parameter lambda. John's prior information regarding lambda (real valued, i.e., a continuous random variable) can be summarized as a continuous uniform PDF in the range from 0 to 0.85. john has recorded his bus waiting times for three days. These are 13, 19, and 26 minutes. Assume that John's bus waiting times in different days are independent. Compute the MAP (maximum a posteriori probability) rule based estimate for lambda given the data collected by John.

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orchestra answered 1 year ago

The number of minutes between successive bus arrivals at Mehmet's bus stop is exponentially distributed with...

The number of minutes between successive bus arrivals at Mehmet's bus stop is exponentially distributed with unknown parameter . Mehmet's prior information regarding (real valued, i.e., a continuous random variable) can be summarized as a continuous uniform PDF in the range from 0 to 0.57. Mehmet has recorded his bus waiting times for three days. These are 26, 11, and 25 minutes. Assume that Mehmet's bus waiting times in different days are independent. Compute the MAP (maximum a posteriori probability) rule...

Lisa is at a bus stop. The times between successive bus arrivals are independent and identically...

Lisa is at a bus stop. The times between successive bus arrivals are independent and identically distributed exponential random variables with mean 3 minutes. While lisa is waiting, Mindy calls to say she will arrive in exactly 3 minutes. Lisa will wait for Mindy and they will ride a bus together. Calculate the probability that Lisa will miss the first and both Lisa and Mindy will catch the second bus.

Suppose that an individual showing up to a bus stop must wait x minutes for a...

Suppose that an individual showing up to a bus stop must wait x minutes for a bus, where x follows a uniform distribution between 0 and 45 minutes. 1. What is the probability that someone will have to wait between 30 and 40 minutes for a bus? 2. If we took many random samples of 50 people waiting for the bus, the sampling distribution of the average wait time of these samples should be normal with a mean of _______...

6.The time of arrivals between two successive cars to a gas station is assumed to have...

6.The time of arrivals between two successive cars to a gas station is assumed to have an exponential distribution with mean 8 minutes. A maintenance operation is started on the road. A random sample of 36 arrival times are recorded to determine the effect of maintenance operation, and average time between arrivals is found as 10 minutes. a) Test the hypothesis that the mean arrival time has changed. Use =0.05. b) Discuss what practical conclusions you would draw in part...

The discrete random variable X is the number of passengers waiting at a bus stop. The...

The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? X 0 1 2 3 Total P(X) .20 .40 .30 .10 1.00 Answer the following questions using the given probability distribution. Expected value E(X) of the number of passengers waiting at the bus stop. Probability that there is at least 1 passenger at the bus stop. Probability...

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The mean time between arrivals of customers in a bank is 3 minutes. Write the expression...

The mean time between arrivals of customers in a bank is 3 minutes. Write the expression for the exponential distribution for average time between arrivals for any time t (t>=0). If a customer has already arrived in the bank, what is the probability that the next customer will come after 10 minutes? What is the probability that 5 customers will arrive in the one hour interval? Answer with full steps. Thank you!, Any half answer or incomplete answer would be...

1-Orders come to a warehouse facility with an exponentially distributed interarrival time of 20 minutes. What...

1-Orders come to a warehouse facility with an exponentially distributed interarrival time of 20 minutes. What is the probability of having no orders during a given hour period?

The number of months that a light bulb is functioning is exponentially distributed with parameter λ...

The number of months that a light bulb is functioning is exponentially distributed with parameter λ = 1/10 . What is the probability that a light bulb will burn for at least 4 months? Find the mean and the standard deviation. What is the probability that a light bulb will burn for at least 12 months, given that it has burned for 4 months?

Phillip was waiting for a bus at a bus stop. Across the street and down the...

Phillip was waiting for a bus at a bus stop. Across the street and down the block, a mechanic negligently overinflated a tire he was intending to put onto Marsha’s pickup truck. The exploding tire injured Marsha and frightened a neighborhood dog, which ran down the street and knocked Phillip down, injuring his knee. Phillip sued the mechanic. In applying the Palsgraf v. Long Island Railroad Co. decision to this case, explain in detail why or why not the mechanic...

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