(R programming)
Generate 50 samples from a Poisson distribution with lambda to
be 2 and define the log likelihood function
Use optimization to find the maximum likelihood estimator of
lambda. Repeat for 100 times using forloop. You will need to save
the results of the estimated values of lambda.
Consider a Poisson distribution in which the offspring
distribution is Poisson with mean 1.3. Compute the (finite-time)
extinction probabilities un = P{ Xn = 0 |
X0 = 1 } for n = 0, 1, . . . , 5. Also compute the
probability of ultimate extinction u∞.
Consider a Poisson probability distribution with
lambda
equals5.3
.
Determine the following probabilities.
a) exactly
5
occurrences
b) more than
6
occurrences
c)
3
or fewer occurrences
For a newsvendor product the probability distribution of demand
X (in units) is as follows:
xi 0 1 2 3 4 5 6
pi 0.05 0.1 0.2 0.3 0.2 0.1 0.05
The newsvendor orders Q = 4 units.
a) Derive the probability distributions and the cumulative
distribution functions of lost sales as well as leftover
inventory.
b) Knowing that the expected total cost function is convex in
the order quantity Q, demonstrate that Q = 4 gives the minimal
expected...
The number of views of a page on a Web site follows a Poisson
distribution with a mean of 1.5 per minute.
(i) What is the probability of no views in a minute?
(ii) What is the probability of two or fewer views in 10
minutes?
(iii) What is the probability of two or fewer views in 2
hours?
The number of airplane landings at a small airport
follows a Poisson distribution with a mean rate of 3 landings every
hour.
4.1 (6%)
Compute the probability that 3 airplanes arrive in a
given hour?
4.2 (7%)
What is the probability that 8 airplanes arrive in three
hours?
4.3 (7%)
What is the probability that more than 3 airplanes
arrive in a period of two hours?
Suppose the number of earthquakes occurring in an area
approximately follows a Poisson distribution with an average rate
of 2 earthquakes every year.
a.) Find the probability that there will be 1 to 3 (inclusive)
earthquakes during the next year in this area.
b.) Find the probability that there will be exactly 5
earthquakes during the next 3 year period.
c.) Consider 10 randomly selected years during last century.
What is the probability that there will be at least 3...
The number of people arriving at an emergency room follows a
Poisson distribution with a rate of 9 people per hour.
a) What is the probability that exactly 7 patients will arrive
during the next hour?
b. What is the probability that at least 7 patients will arrive
during the next hour?
c. How many people do you expect to arrive in the next two
hours?
d. One in four patients who come to the emergency room in
hospital.
Calculate...
The number of people crossing at a certain traffic light follows
a Poisson distribution with a mean of 6 people per hour. An
investigator is planning to count the number of people crossing the
light between 8pm and 10pm on a randomly selected 192 days. Let Y
be the average of the numbers of people to be recorded by the
investigator.
What is the value of E[Y ]?
A. 6 B. 12 C. 1152 D. 0.03125.
What is the value...
If student arrivals to the school dining commons follows the
Poisson distribution with a mean of 50 students per day. For a
randomly selected 36 days: (use 4 digits after decimal
point)
What is the probability that they served breakfast to at least
1757 students during these 36 days? [hint: P(ΣX ≥
1757 students) =?]