Question

The number of alpha particles emitted by a lump of uranium in a given minute is

modeled by a Poisson random variable with parameter l = 1.4. What is the probability that the

uranium atom emits exactly 2 alpha particles in the next minute?

Answer #1

To calculate the required probability we will usw poission distribution.

The half-life of 235U, an alpha emitter, is 7.1×10^8yr.
Calculate the number of alpha particles emitted by 1.5 mg of this
nuclide in 1.0 minute.

A mcg of U-238 emits particles according to a Poisson process at
rate 2/sec. A mcg of U-235 emits particles according to a Poisson
process at rate 10/sec. Marie receives a gift of 1 mcg uranium,
which is U-238 with probability 0.5 and U-235 with probability
0.5.
(a) Marie observes the gift for one second. What is the
probability that no particles are emitted?
(b) Suppose Marie observes that 15 particles are emitted from
her mcg of uranium during a...

Suppose that on the average the number of particles emitted
from a radioactive substance is five per second. What is the
probability that it will take less than 3 seconds for the next two
particles to be emitted?
A beam of length 1 , rigidly supported at both ends,
is hit suddenly at a random point, which leads to a break at a
position X from the right end. If the distribution of X is beta,
with =4, β=2 , what...

In the problem, make sure that you are clearly defining random
variables, stating their distributions, and writing down the
formulas that you are using. (That is, write down the pmf, write
down mean and variance formulas.)
The number of particles emitted by a radioactive source over the
course of an hour is generally well modeled by a Poisson
distribution. (We will see some solid justification of this later
on when we discuss the gamma and exponential distributions.)
Suppose that the...

An insurance company supposes that the number of accidents that
each of its policyholders will have in a year is Poisson
distributed. The rate parameter of the Poisson is also a random
variable which has an exponential distribution with parameter 2.8.
What is the probability that a randomly chosen policyholder has
exactly 2 accidents next year?(Hint: You can use the following
result for thenth moment of exponential random variable:
If Z ∼Exp(μ) , then E (Zn )= n!/μn)

An insurance company supposes that the number of accidents that
each of its policyholders will have in a year is Poisson
distributed. The rate parameter of the Poisson is also a random
variable which has an exponential distribution with parameter 2.3.
What is the probability that a randomly chosen policyholder has
exactly 3 accidents next year?(Hint: You can use the following
result for thenth moment of exponential random variable:
If Z ∼Exp(μ) , then E (Zn )= n!/μn)

The number of automobiles entering a tunnel per 2-minute period
follows a Poisson distribution. The mean number of automobiles
entering a tunnel per 2-minute period is four. (A) Find the
probability that the number of automobiles entering the tunnel
during a 2- minute period exceeds one. (B) Assume that the tunnel
is observed during four 2-minute intervals, thus giving 4
independent observations, X1, X2, X3, X4, on a Poisson random
variable. Find the probability that the number of automobiles
entering...

6. Let N be the number of aerosol particles in a given volume of
air. If the mean number M is a known constant, then it may be
assumed that N has a Poisson distribution. However, M is random and
follows a gamma Γ(n, λ) law. Using conditional expectation, or
otherwise, determine the probability generating function of N, and
hence identify its distribution.

A device that detects the presence of radon gas in a home counts
the number of alpha particles that hit its detector over a defined
period. In a particular home, the number of alpha particles
detected per week averages 3 over a long period of time. Let X
represent the number of alpha particles that will be detected next
week.
a) Suggest a suitable probability model for the random variable
X. Justify your answer and identify any assumptions you are...

The number of tickets issued by a meter reader for parking-meter
violations can be modeled by a Poisson process with a rate
parameter of five per hour. What is the probability that exactly
three tickets are given out during a particular hour? Find the mean
and standard deviation of this distribution.
P(X=3) = 0.1404
Mean = 5
Standard deviation = 2.2361
UNANSWERED: What is the probability that
exactly 10 tickets are given out during a particular 3-hour
period?

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