Question
In: Statistics and Probability
A radioactive mass emits particles according to a Poisson process at a mean rate of 2.5...
A radioactive mass emits particles according to a Poisson process at a mean rate of 2.5 per second. Let T be the waiting time, in seconds, between emissions.
1-What is the median waiting time?
2-Find P(0.3 < T < 1.5).
3-If 3 seconds have elapsed with no emission, what is the probability that there will be an emission within the next second
Solutions
1.
3.
orchestra answered 2 years agoRelated Solutions
In a certain decay process, a nucleus in the vicinity of mass 240 emits alpha particles...
In a certain decay process, a nucleus in the vicinity of mass
240 emits alpha particles with the following energies (in MeV):
5.545 ( ao), 5.513 ( al), 5.486( a2), 5.469 ( a3), 5.443 (a4),
5.417 (a5), and 5.389 (a6). The following gamma rays in the
daughter nucleus are seen (energies in keV): 26 (g1), 33(g2),
43(g3), 56(g4), 60(g5), 99(g6), 103(g7), 125(g8). Construct a decay
scheme from this information, assuming a0. populates the ground
state of the daughter. Keep in...
Customers arrive at a service center according to a Poisson process with a mean interarrival time...
Customers arrive at a service center according to a Poisson
process with a mean interarrival
time of 15 minutes.
If two customers were observed to have arrived in the first
hour, what is the probability that at least
one arrived in the last 10 minutes of that hour?
People arrive at a party according to a Poisson process of rate 30 per hour and...
People arrive at a party according to a Poisson process of rate
30 per hour and remain for an independent exponential time of mean
2 hours. Let X(t) be the number of people at the party at time t
(in hours) after it started. Compute E[X(t)] and determine how long
it takes to have on average more than 40 people at the party.
Emails arrive in an inbox according to a Poisson process with rate λ (so the number...
Emails arrive in an inbox according to a Poisson process with
rate λ (so the number of emails in a time interval of length t is
distributed as Pois(λt), and the numbers of emails arriving in
disjoint time intervals are independent). Let X, Y, Z be the
numbers of emails that arrive from 9 am to noon, noon to 6 pm, and
6 pm to midnight (respectively) on a certain day. (a) Find the
joint PMF of X, Y, Z....
Students enter the bathroom according to a Poisson process at a rate of 7.5 arrivals per...
Students enter the bathroom according to a Poisson
process at a rate of 7.5 arrivals per minute.
What is the probability that exactly 46 students enter
between 3:00 and 3:05?
Given that 6 students enter the bathroom between 4:00
and 4:01, what is the probability that exactly 36 students enter
between 4:00 and 4:07?
Each student entering the bathroom has a .15 probability
of wearing a hoodie, independent of other students. What is the
probability that exactly 10 students wearing...
Small aircraft arrive at a private airport according to a given Poisson process at a rate...
Small aircraft arrive at a private airport according to a given
Poisson process at a rate of 6 per hour.
What is the probability that exactly 5 small aircraft arrive in
the first hour (after opening) and exactly 7 arrive in the hour
after that?
What is the probability that fewer than 5 small aircraft arrive
in the first hour and at least 10 arrive in the hour after
that?
What is the probability that exactly 5 small aircraft arrive...
Customers are arriving to a shop according to Poisson process with mean 3.2 customers/hour. What is...
Customers are arriving to a shop according to Poisson process
with mean 3.2 customers/hour. What is the probability that the next
customer will arrive after 10 minutes but before 33 minutes?
(20 pts) Inquiries arrive at an information center according to a Poisson process of rate 2...
(20 pts) Inquiries arrive at an information center according to
a Poisson process of rate 2 inquiries per second. It takes a server
an exponential amount of time with mean ½ second to answer each
query.
(a) (5 pts) If there are two servers. What is the probability
that an arriving customer must wait to be served?
(b) (5 pts) Find the mean number of customers in the system and
the mean time spent in the system.
(c) (10 pts)...
Calls to an agency come according to a rate λ Poisson process. The agency has s...
Calls to an agency come according to a rate λ Poisson process.
The agency has s telephone lines and the duration of each call is
an exponential random variable with parameter µ. If a call comes
when all lines are busy, it is not taken or put on hold. Find the
stationary distribution of the number of busy lines.
Calls to an agency come according to a rate λ Poisson process. The agency has s...
Calls to an agency come according to a rate λ Poisson process.
The agency has s telephone lines and the duration of each call is
an exponential random variable with parameter µ. If a call comes
when all lines are busy, it is not taken or put on hold. Find the
stationary distribution of the number of busy lines.
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Use the bond term's below to answer the question Maturity 7 years Coupon Rate 4% Face...
- What experience have you had with Organization Development or with Change Management? Describe the organization, the...
- 1. Renfro Rentals has issued bonds that have a 12% coupon rate, payable semiannually. The bonds...
- Given an array of positive integers a, your task is to calculate the sum of every...
- Define “culture.” Software is defined by the Merriam-Webster Dictionary as "the programs that run on a...
- In humans, hypotrichosis (sparse body hair) is a rare autosomal recessive condition. Let h = hypotrichosis...
- Increase all of the listing prices by 5% for all listings under $500,000 and 10% for...
ADVERTISEMENT