Suppose that events occur in accordance with a Poisson process at the rate of five events per hour a Determine the distribution of the waiting time T1 until the first event occurs b Determine the distribution of the total waiting time Tk until k events have occurred c Determine the probability that none of the first k events will occur within 20 minutes of one another

Question: Suppose that events occur in accordance with a Poisson process at the rate of five events per hour. a. Determine the distribution of the waiting

Suppose that events occur in accordance with a Poisson process at the rate of five events per hour.
a. Determine the of the waiting time T1 until the first event occurs.
b. Determine the of the total waiting time Tk until k events have occurred.
c. Determine the probability that none of the first k events will occur within 20 minutes of one another.

Step by Step Solution

★★★★★

3.33 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a PrT 1 t PrX 0 where X is the number of occurrences between time 0 and ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

602-M-S-D-D (773).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Use the dependency diagram shown in Figure 6.8 to work the following problems. a. Break up the dependency diagram in Figure 6.8 to create two new dependency diagrams, one in 3NF and one in 2NF. b....

Customers arrive at a single-server queueing system in accordance with a Poisson process with an expected interarrival time of 25 minutes. Service times have an exponential distribution with a mean...

The number of cars that arrive at a banks drive-through window between 3:00 p.m. and 6:00 p.m. on Friday follows a Poisson process at the rate of 0.41 car every minute. Compute the probability that...

Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport,...

1.A random variable x has the following probability distribution. Determine the expected value of x. x f(x) 0 0.03 1 0.12 2 0.3 3 0.2 4 0.35 2.random variable x has the following probability...

3. (a) During lunch hour, arrivals of customers at a pizza hut restaurant follows a Poisson process with the rate of 120 customers per hour. The restaurant has one line, with three workers taking...

Create program, first, prompt the user for a # of years to enter for a player. Then, prompt the user for the player's starting year and then read in the statistics of the player for each of those...

3. (a) During lunch hour, arrivals of customers at a pizza hut restaurant follows a Poisson process with the rate of 120 customers per hour. The restaurant has one line, with three workers taking...

Table: Lq Values for the Multi-server Queue Values of Lq for s servers, with mean utilization rate r, assuming Poisson arrivals and exponential service times. Utilization 0.10 0.20 0.30 0.35 0.40...

5. Messages arrive at a telegraph office as a Poisson process with mean rate of 3 messages per hour. What is the i) ii) Probability that no messages arrive during the morning hours 8:00 A.M. to noon?...

Consider a queueing system with two servers A and B where jobs arrive as a Poisson process at a rate of 20 jobs per hour. It takes server A an exponentially distributed amount of time with a mean of...

Figure 11-31 shows a cooling curve for a Pb-Sn alloy. Determine (a) The pouring temperature; (b) The superheat; (c) The liquidus temperature; (d) The eutectic temperature; (e) The freezing range; (f)...

Return to questlon 1 2. List the accounts and amounts that would appear on the 31 March statement of financial position. Data regarding Petrilla Corp. In March 20X9: Answer is complete but not...

In a defined - benefit pension plan, who assumes the risk? state government the federal government the employer the employee

Refrigerant-22 at 180 F, x = 0.1 flowing at 4 lbm/s is brought to saturated vapor in a constant-pressure heat exchanger. The energy is supplied by a heat pump with a low temperature of 50 F. Find the...

A cylinder fitted with a movable piston contains water at 3 MPa, 50% quality, at which point the volume is 20 L. The water now expands to 1.2 MPa as a result of receiving 600 kJ of heat from a large...

A wet cooling tower is to cool 60 kg/s of water from 40 to 26°C. Atmospheric air enters the tower at 1 atm with dry- and wet-bulb temperatures of 22 and 16°C, respectively, and leaves at...

Figure P31.68 shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 50.0 cm. It is placed in a constant magnetic field of 0.500 T directed out...

A well-insulated rigid tank contains 2 kg of a saturated liquidvapor mixture of water at 100 kPa. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in...

4. Explain the differences in using linear regression to develop a time series forecasting model and a causal forecasting model.

Let X have a Weibull distribution with the pdf from Expression (4.11). Verify that = B(1+1/). [In the integral for E(X), make the change of variable y = (x/), so that x = By 1 / .]

The article "The Statistics of Phytotoxic Air Pollutants" (J. of Royal Stat. Soc., 1989: 183-198) suggests the lognormal distribution as a model for SO2 concentration above a certain forest. Suppose...

The authors of the article from which the data in Exercise 1.27 was extracted suggested that a reasonable probability model for drill lifetime was a lognormal distribution with = 4.5 and = .8. a....

The Women's Health Study included 39,876 female health professionals aged 45 years and older who were followed for an average of 10 years (Ridker et al., 2005). At the beginning of the study,...

The owner of the Krusty Krab is considering selling his restaurant and retiring. An investor has offered to buy the Krusty Krab for $350,000 whenever the owner is ready for retirement. The owner is...

with explanation Which chart is used to illustrate patterns of data collected over time and is intended to indicate patterns