Question

**1. Suppose the number of junk emails you received per
day has a Poisson distribution with** **an average of
five per day.**

**a) What is the probability that you receive 3 junk
emails per day?**

**b) What is the probability that you receive at least 1
junk email per day?**

**c) What is the probability that you receive at most 3
junk emails per day?**

**d) What is the likelihood of receiving between 3 and 6
junk emails per day?**

Answer #1

a)

this is Poisson distribution with parameter
λ=5 |

**probability that you receive 3 junk emails per day
=P(X=3) =e ^{-5}*5^{3}/3! =0.1404**

**b)**

**probability that you receive at least 1 junk email per
day =P(X>=1)=1-P(X=0)
=1-e ^{-5}*5^{0}/0!**

**=1-0.0067 =0.9933**

**c(**

**probability that you receive at most 3 junk emails per
day =P(X<=3)**

**=P(X=0)+P(X=1)+P(X=2)+P(X=3)**

**=e ^{-5}*5^{0}/0!
+e^{-5}*5^{1}/1! +e^{-5}*5^{2}/2!
+e^{-5}*5^{3}/3!**

**=0.0067+0.0337+0.0842+0.1404=0.2650**

**d)**

**P(3<=X<=6)
=P(X=3)+P(X=4)+P(X=5)+P(X=6)**

**=e ^{-5}*5^{3}/3!+e^{-5}*5^{4}/4!+e^{-5}*5^{5}/5!+e^{-5}*5^{6}/6!
=0.6375**

The number of spam emails received each day follows a Poisson
distribution with a mean of 50. Approximate the following
probabilities. Apply the ±½ correction factor and round value of
standard normal random variable to 2 decimal places.
Round your answer to four decimal places (e.g. 98.7654).
(a) More than 50 and less than 60 spam emails in a
day.
(b) At least 50 spam emails in a day.
(c) Less than 50 spam emails in a day.
(d) Approximate...

Suppose that the number of spam emails that Alex receives has a
Poisson distribution with µ = 2.3 per day. What is the probability
that the number of spam emails Alex receives in a day is within one
standard deviation of the mean? Clearly state the random variable
of interest using the context of the problem and what probability
distribution it follows.

The number of emails that I get in weekday can be
modeled by a Poisson distribution with an average of 0.2 emails per
minute.
1. What is the probability that I get no emails in an
interval of length 5 minutes?
2. What is the probability that I get more than 3 emails
in an interval of length 10 minutes?

According to a 2017 survey conducted by the technology market
research firm The Radicati Group, U.S. office workers receive an
average of 121 emails per day.† Suppose for a particular office the
number of emails received per hour follows a Poisson distribution
and that the average number of emails received per hour is seven.
(Round your answers to four decimal places.)
(a)
What is the probability of receiving no emails during an
hour?
(b)
What is the probability of receiving...

With an average of 2.5 per day following Poisson distribution,
what is the probability that the next day there is only 1?
What is the probability that there is at least 2 the next
day?
What is the probability that there are at most 2 the next day?

A household receives an average of 3 pieces of junk mail per
day. What is the probability that this household will not receive
any junk mail on a certain day? will receive exactly 10 junk mails
in 4 days? will receive at least 4 junk mails in two days?

Q: If you receive on average 2 spam emails per day, what is the
probability that you don't receive any spam email on a given
day?
Q: Given P(X)=0.2 P(X)=0.2, P(Y)=0.3 P(Y)=0.3 and P(X∩Y)=0.1
P(X∩Y)=0.1, what is P(X|Y)P(X|Y)?
Q: What is the smallest possible sample mean of a bootstrap
sample that you can obtain from the sample [1,2,3,4,5]?
Q: An insurance company records on average 10 CTP claims per
day. What is the probability that on a particular day at...

Suppose that the number of accidents occurring on a highway per
hour follows a Poisson distribution with a mean of 1.25.
What is the probability of exactly three accidents occur in
hour?
What is the probability of less than two accidents in ten
minutes?
What is the probability that the time between two successive
accidents is at least ten minutes?
If ten minutes have gone by without an accident, what is the
probability that an accident will occur in the...

Suppose that the number of accidents occurring on a highway per
hour follows a Poisson distribution with a mean of 1.25.
What is the probability of exactly three accidents occur in
hour?
What is the probability of less than two accidents in ten
minutes?
What is the probability that the time between two successive
accidents is at least ten minutes?
If ten minutes have gone by without an accident, what is the
probability that an accident will occur in the...

Suppose that the number of Wi-fi interruptions in your home
network follows the Poisson distribution with an average of 1.5 per
day.
a. Calculate the probability that will have exactly 2
interruptions tomorrow.
b. Calculate the probability that you will have at least 2
interruptions tomorrow.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 8 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 23 minutes ago

asked 31 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago