Radiation: The atoms of a radioactive element are randomly disintegrating and
emitting alpha particles. The number of alpha particles emitted per second from
these atoms during a 30 second period is recorded as follows.
9.38
8.08
8.36
10.44
9.44
8.05
17.78
7.56
14.17
6.73
9.81
4.79
11.98
9.48
6.32
14.23
13.02
5.99
7.05
11.62
10.81
7.94
9.47
12.05
7.78
12.95
6.87
16.65
10.73
10.33

Trying to find best mathematical distribution model that fits the process

1 Assume that this alpha particle emission process follows a Poisson distribution. Find the parameters of this Poisson distribution. For a
Poisson distribution <x>=lambda and variance=square root of lambda)

Is this a good approximation?

2 Find a Gaussian distribution that approximates the number of alpha
particles emitted from these atoms per second.

3 Which distribution approximates the data more accurately? What is your measure of accuracy?

4 What is the probability of having more than 12 alpha particles emitted from these atoms per second? (Have you decided which distribution best describes the data?)

Let X have a Poissondistribution with a mean of 4. Find
a) P(23)
c) P(X<3)
Let X have a Poissondistribution with a variance of 4. Find P(X=2)
Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poissondistribution, give the probability th

The random variable X has a Poissondistribution with a mean of 5. The random variable Y has a binomial distribution with n=X and p=1/2.
a) Find the mean and variance of Y.
b) Find P(Y=0)

Please help with following question:
During normal business hours on the east coast, calls to the toll-free reservation number of the Nite Time Inn that the numb roy calls per minute can be described by the Poissondistribution. Find the probability that in the next minute, the number of calls arriving will be 5, 4, 3, 6, le

A baseball team loses $10,000 for each consecutive day it rains, Say X, the number of consecutive days it rains at the beginning of the season, has a Poissondistribution with mean 0.2. What is the expected loss before the opening game?
An airline always overbooks if possible. A particular plane has 95 seats on a flight in wh

An internal study by the technology service4 department at lahey electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poissondistribution.
1. What is the probability Linda Lahey, company president, received exactly 1 email between 4 pm and

Central Limit Theorem Exercise
Write a computer program or Excel spreadsheet that:
a. takes a given distribution function (f(x), as given below), for x between: 0 and 1.0,
b. randomly samples this function at n points and determines the mean for that sample
c. repeats b. N times
d. plots a histogram of the result of the

In Bombay, India air pollution standards for particulate matter are exceeded an average of 5.6 days in every 3 week period. Assume that the distribution of the number of days exceeding the standards per three week period is Poisson distributed.
What is the probability that the standard is not exceeded on any day during a thr

See attached file.
A coin is flipped. If the outcome is heads you draw a number form a Gaussiandistribution with mean 0 and variance 1. If the outcome is tails you draw a number from a uniform [0,1] distribution. What is the mean and variance of the distribution for the number you will generate?

True or false: Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.0504.