LEARN MORE...

Access Millions of academic & study documents

ECEN 403 Conditional Probability Exercises

Content type
User Generated
Subject
Statistics
Type
Other
Showing Page:
1/11
CIVL/ECEN-403/MECH-328
Assignment # 3 Probability and Statistics for Engineers Summer 2019 -
20
Due Date: Sunday, August 30, 2020
Following problems cover the topic on Conditional Probability.
Q1: A class in advanced physics is composed of 10 juniors, 30 seniors, and 10
graduate students. The final grades show that 3 of the juniors, 10 of the seniors,
and 5 of the graduate students received an A for the course. If a student is
chosen at random from this class and is found to have earned an A, what is the
probability that he or she is a senior?
Q2: A random sample of 200 adults are classified below by sex and their
level of education attained.
If a person is picked at random from this group, find the probability that
(a)
the person is a male, given that the person has a secondary education;
(b)
the person does not have a college degree, given that the person is a female.
Q3: For married couples living in Al Buraimi, the probability that the husband
will vote on Shura Election is 0.21, the probability that the wife will vote is 0.28,
and the probability that both the husband and the wife will vote is 0.15. What is
the probability that
(a)
at least one member of a married couple will vote?
(b)
a wife will vote, given that her husband will vote?
(c)
a husband will vote, given that his wife will not vote?
Following problems cover the topic on Discrete Random Variables.
Q4: A shipment of 20 similar laptop computers to a retail outlet contains 5 that are
defective. A school makes a random purchase of 3 of these computers. Let 𝑋 be the
number of defectives in the sample of 3. Find the probability distribution for 𝑋.

Sign up to view the full document!

lock_open Sign Up
Showing Page:
2/11
−1
Q5: Let 𝑊 be a random variable giving the number of heads in three tosses of a coin.
(a) List the elements of the sample space 𝑆 for the three tosses of the coin and to each
sample point assign a value 𝑤 of 𝑊.
(b) To each sample point 𝑤, associate its probability 𝑃(𝑤).
(c) Find the mean
𝜇
=
𝐸
(
𝑊
) and the variance
𝜎
2
=
𝐸
(
𝑊
2
)
−
[
𝐸
(
𝑊
)]
2
Following problems cover the topic on Continuous Random Variables.
Q6: Let 𝑋 be a continuous random variable whose probability density function is given by
(a) Verify that 𝑓(𝑥) is actually a probability density
function;
(b) Find
𝑃
(0 <
𝑋
< 1) and
𝑃
(
𝑋
> 1).
(c) Find the mean 𝐸(𝑋) and the variance 𝑉𝑎𝑟(𝑋).
Q7: Given 𝑓
(
𝑥
)
=
{
𝑘𝑥
2
,
−1 <
𝑥
<
3
0,
𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
(a) Find 𝑘 so that the function 𝑓(𝑥) is a probability density function of a continuous random variable
𝑋.
(b) Find the distribution function 𝐹(𝑥).
Hint: Recall that
𝐹
(
𝑥
)
=
𝑃
(
𝑋
≤
𝑥
)
=
∫
𝑓
(
𝑡
)
𝑑
𝑡
.
Have Fun
Q1)

Sign up to view the full document!

lock_open Sign Up
Showing Page:
3/11

Sign up to view the full document!

lock_open Sign Up
End of Preview - Want to read all 11 pages?
Access Now
Unformatted Attachment Preview
Assignment # 3 CIVL/ECEN-403/MECH-328 Probability and Statistics for Engineers 20 Summer 2019 - Due Date: Sunday, August 30, 2020 Following problems cover the topic on Conditional Probability. Q1: A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students. The final grades show that 3 of the juniors, 10 of the seniors, and 5 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that he or she is a senior? Q2: A random sample of 200 adults are classified below by sex and their level of education attained. If a person is picked at random from this group, find the probability that (a) the person is a male, given that the person has a secondary education; (b) the person does not have a college degree, given that the person is a female. Q3: For married couples living in Al Buraimi, the probability that the husband will vote on Shura Election is 0.21, the probability that the wife will vote is 0.28, and the probability that both the husband and the wife will vote is 0.15. What is the probability that (a) at least one member of a married couple will vote? (b) a wife will vote, given that her husband will vote? (c) a husband will vote, given that his wife will not vote? Following problems cover the topic on Discrete Random Variables. Q4: A shipment of 20 similar laptop computers to a retail outlet contains 5 that are defective. A schoo ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.
Studypool
4.7
Indeed
4.5
Sitejabber
4.4

Similar Documents

1.Compute the weighted mean for the following data.
Week 2 Assignment Question 1 1.Compute the weighted mean for the following data. Question 2 1.If P(A) = 0.5...
Probability Worksheet, statistics homework help
I added a file...
American University Linear Relationship in Mathematical Problems Questions
EXAM 1 REVIEW 𝑥 𝑦 1 5 3 5 6 7 11 17 20 23 Could the above data be linear? If so, what’s the slope? If not, ex...
Use Sigma notation to represent the series below, statistics homework help
Use Sigma notation to represent the series below....
ISE 2404 VTU Deterministic Operations Research Worksheet
ISE 2404 – Deterministic Operations Research I • You will be graded both on mathematical solutions to the problems al...
Anchorage Restaurant Business Plan
Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, ...
Probability Answers
Q1: We have n data and denote them by x1, x2,..,xn. If we write its harmonic mean by mH, write...
Factorial Problem
Consecutive zeros, or trailing zeros are made when a multiple of 5 is Pairs of 2 and 5 form trailing zeroes, since we only...
Final Answer
...