QI. An engineer or scientist is measuring the output of a pin of an IC. It turns out that the outputs are cither 0 or 1 (onc can think of 0 as 0 volts and 1 as the 5 volts). The engineer /scientist is informed that the output is governed by a probability mass function. Therefore, the output can be treated as a random variable and since the outcomes belong to the set {0,1}, it is a discrete random variable (we denote it by X). It turns out that the probability of getting X=1 is 0.3, i.e., p(x=1)=P, where P=0.3. The probability mass function is given as follows x = 0 x = 1' where P= 0.3. This pmf can also be represented as (1- P, f(x) = {p f(x)=P*(1-P)-. a) Find the mean (expected value) of X. This means that what do we get in the output, on the average. b) Find the variance of the random variable X c) Now the engineer/scientist, starts measuring the output. He/she repeats the process 20 times. The outcomes are as follows. X = [1 0 0 0 0 0 o 0 1 0 11 110 0 0 0 1 o] c-1) Plot the histogram of data
QI. An engineer or scientist is measuring the output of a pin of an IC. It turns out that the outputs are cither 0 or 1 (onc can think of 0 as 0 volts and 1 as the 5 volts). The engineer /scientist is informed that the output is governed by a probability mass function. Therefore, the output can be treated as a random variable and since the outcomes belong to the set {0,1}, it is a discrete random variable (we denote it by X). It turns out that the probability of getting X=1 is 0.3, i.e., p(x=1)=P, where P=0.3. The probability mass function is given as follows x = 0 x = 1' where P= 0.3. This pmf can also be represented as (1- P, f(x) = {p f(x)=P*(1-P)-. a) Find the mean (expected value) of X. This means that what do we get in the output, on the average. b) Find the variance of the random variable X c) Now the engineer/scientist, starts measuring the output. He/she repeats the process 20 times. The outcomes are as follows. X = [1 0 0 0 0 0 o 0 1 0 11 110 0 0 0 1 o] c-1) Plot the histogram of data
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
![Q1. An engineer or scientist is measuring the output of a pin of an IC. It turns out that the outputs are
either 0 or 1 (one can think of 0 as 0 volts and 1 as the 5 volts). The engineer /scientist is informed that
the output is governed by a probability mass function. Therefore, the output can be treated as a random
variable and since the outcomes belong to the set {0,1}, it is a discrete random variable (we denote it by
X). It turns out that the probability of getting X=1 is 0.3, i.e., p(x=1)=P, where P=0.3. The probability
mass function is given as follows
x = 0
x = 1'
(1- P,
f(x) = {P,
where P= 0.3. This pmf can also be represented as
%3D
f(x)=P*(1-P)--×.
a) Find the mean (expected value) of X. This means that what do we get in the output, on the
average.
b) Find the variance of the random variable X
c) Now the engineer/scientist, starts measuring the output. He/she repeats the process 20 times. The
outcomes are as follows.
X = [1 0 0 0 0 o o 0 1 0 11 1 1 0 0 0 0 1 o]
c-1) Plot the histogram of data
c-2) Normalize the histogram and plot it.
c-3) Find the mean and variance of the collected samples. Find the probability of p(X=1) from the
collected measurements (is this the same as the actual probability P?). Compare the results with the actual
mean and variances. Are they different? Explain what you learned from this problem.
c-4) Represent the data with the approximated pmf (look at the actual pmf and instead of P use the
probability of p(X=1) you found from the data). Plot the approximated and the actual pmfs.
Note: The random variable in this problem is called Bernoulli. Meaning that X is governed by a Bernoulli
distribution. In most real world problems, we do not now the actual distribution of our data. However, we
can model our data via a famous distribution (such as Bernoulli) based on the samples we get (look at
what you did in part c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F199d58c4-213a-4e42-b645-d01318acf93a%2F84b6bb64-0cd1-4f2a-a793-05b00eb80670%2F706am5o_processed.png&w=3840&q=75)
Transcribed Image Text:Q1. An engineer or scientist is measuring the output of a pin of an IC. It turns out that the outputs are
either 0 or 1 (one can think of 0 as 0 volts and 1 as the 5 volts). The engineer /scientist is informed that
the output is governed by a probability mass function. Therefore, the output can be treated as a random
variable and since the outcomes belong to the set {0,1}, it is a discrete random variable (we denote it by
X). It turns out that the probability of getting X=1 is 0.3, i.e., p(x=1)=P, where P=0.3. The probability
mass function is given as follows
x = 0
x = 1'
(1- P,
f(x) = {P,
where P= 0.3. This pmf can also be represented as
%3D
f(x)=P*(1-P)--×.
a) Find the mean (expected value) of X. This means that what do we get in the output, on the
average.
b) Find the variance of the random variable X
c) Now the engineer/scientist, starts measuring the output. He/she repeats the process 20 times. The
outcomes are as follows.
X = [1 0 0 0 0 o o 0 1 0 11 1 1 0 0 0 0 1 o]
c-1) Plot the histogram of data
c-2) Normalize the histogram and plot it.
c-3) Find the mean and variance of the collected samples. Find the probability of p(X=1) from the
collected measurements (is this the same as the actual probability P?). Compare the results with the actual
mean and variances. Are they different? Explain what you learned from this problem.
c-4) Represent the data with the approximated pmf (look at the actual pmf and instead of P use the
probability of p(X=1) you found from the data). Plot the approximated and the actual pmfs.
Note: The random variable in this problem is called Bernoulli. Meaning that X is governed by a Bernoulli
distribution. In most real world problems, we do not now the actual distribution of our data. However, we
can model our data via a famous distribution (such as Bernoulli) based on the samples we get (look at
what you did in part c).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON