Question

In: Math

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.

Solutions

Expert Solution

3minute is the Time interval is taken, and average number of bus arrival in the given time period is 1, so the event (bus arrives) follows Poisson (1).

milcah answered 1 year ago
Next > < Previous

Related Solutions

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...
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...
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 time between successive arrivals of calls to emergency service is random variable which follows exponential...
The time between successive arrivals of calls to emergency service is random variable which follows exponential distribution. It was observed that on average calls arrive to emergency service every four minutes (1 / λ = 4min) and average number of calls in one minute is λ = 0.25 calls/ 1 min The probability that the time between successive calls is less than 2 minutes is ______ The probability that the time between successive calls is less than 2 minutes is...
Question 4: The times that a cashier spends processing each person’s transaction are independent and identically...
Question 4: The times that a cashier spends processing each person’s transaction are independent and identically distributed random variables with a mean of µ and a variance of σ2 . Thus, if Xi is the processing time for each transaction, E(X i) = µ and Var(Xi) = σ2 . Let Y be the total processing time for 100 orders: Y = X1 + X2 + · · · + X100 (a) What is the approximate probability distribution of Y ,...
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...
. In his quest to test whether interval times (x minutes) between arrivals of vehicles at...
. In his quest to test whether interval times (x minutes) between arrivals of vehicles at a busy transport terminal are exponentially distributed with parameter β, an investigator collected one hundred such interval times as shown in the table below Time Interval (mins) 0 – 4.99 5 – 9.99 10 – 14.99 15 – 24.99 25 – 39.99 40 Cars 22 15 18 16 11 18 Note that x¯ = 10 a. State the null and the alternative hypotheses for...
A comparison is made between two bus lines to determine if arrival times of their regular...
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 61 randomly selected runs, bus line B was observed to be off schedule an average of 62 minutes, with standard deviation 11 minutes. Do...
A comparison is made between two bus lines to determine if arrival times of their regular...
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 19 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 61 minutes, with standard deviation 13 minutes. Do...
A comparison is made between two bus lines to determine if arrival times of their regular...
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 46randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 15 minutes. For 61 randomly selected runs, bus line B was observed to be off schedule an average of 62 minutes, with standard deviation 13 minutes. Do the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT