lecture#1 probability distribution .pptx

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The document outlines the basics of applied statistics, focusing on discrete probability distributions and random variables. It includes definitions, distinctions between discrete and continuous distributions, and formulas for calculating mean, variance, and standard deviation. The document also provides examples and characteristics related to different types of random variables.

(MT-503)
LECTURE NO.1
APPLIED STATISTICS

1-2
REFERENCE BOOKS
 ELEMENTARY STATISTICS BY ALAN G.
BLUMAN (8TH EDITION).
 PROBABILITY AND STATISTICS FOR
ENGINEERS & SCIENTISTS BY WALPOLE
& MYERS YE. (9TH EDITION).
 APPLIED STATISTICS & PROBABILITY
FOR ENGINEERS, BY Douglas C.
Montgomery , George C. Runger.

©The McGraw-Hill Companies, Inc. 2008
McGraw-Hill/Irwin
Discrete Probability Distributions
RANDOM VARIABLE

4
1. Define the terms probability distribution and
random variable.
2. Distinguish between discrete and continuous
probability distributions.
3. Calculate the mean, variance, and
standard deviation of a discrete
probability distribution.
4. Describe the characteristics of and
compute probabilities using the binomial
probability distribution.
5. Describe the characteristics of and
compute probabilities using the Poisson
probability distribution
6. Describe the characteristics of and compute
probabilities using the –ve binomial and
GOALS

What is a Probability Distribution?
Experiment:
Toss a coin three
times. Observe the
number of heads.
The possible results
are: zero heads, one
head, two heads,
and three heads.
What is the
probability
distribution for the
number of heads?
5

Probability Distribution of Number of
Heads Observed in 3 Tosses of a Coin
6

Characteristics of a Probability
Distribution
7
1. The probability of a
particular outcome is
between 0 and 1 inclusive.
2. The outcomes are
mutually exclusive
events.
3. The list is exhaustive. The
sum
of the probabilities of the

Random Variables
Random variable :A real valued
function define on sample is called
random variable..
8

Types of Random Variables
9
 Discrete Random Variable can assume
only certain clearly separated values. It is
usually the result of counting something
 Continuous Random Variable can assume
an infinite number of values within a
given range. It is usually the result of
some type of measurement

Discrete Random Variables - Examples
The number of students in a class.
The number of children in a family.
The number of cars entering a
carwash in a hour.
Number of home mortgages
approved by Coastal Federal Bank
last week.
10

Continuous Random Variables -
Examples
11
 The length of each song on the latest
Tim McGraw album.
 The weight of each student in this
class.
 The temperature outside as you are
reading this book.
 The amount of money earned by each of
the more than 750 players currently on
Major League Baseball team rosters.

Prob. Mass function (pmf):
 f(x) = P(X=x)
12

The Mean of a discrete Probability
Distribution
Mean
•The mean is a typical value used to
represent the central location of a
probability distribution.
•The mean of a probability
distribution is also referred to as its
expected value.
13

The Variance, and Standard Deviation of
a Discrete Probability Distribution
14

Mean, Variance, and Standard Deviation of a
Discrete Probability Distribution - Example
John Ragsdale sells new cars for Pelican Ford.
John usually sells the largest number of
cars on Saturday. He has developed the
following probability distribution for the
number of cars he expects to sell on a
particular Saturday.
15

Mean of a Discrete Probability Distribution -
Example
16

Variance and Standard Deviation of a Discrete
Probability Distribution - Example
 1.290 
1.135
17

2



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This PowerPoint presentation is based on Unit 7 – Assisting Individuals and Families to Promote and Maintain Their Health, a core topic in Community Health Nursing – I for 5th Semester B.Sc Nursing students, as per the Indian Nursing Council (INC) guidelines. The unit emphasizes the nurse’s role in family-centered care, early detection of health problems, health promotion, and appropriate referrals, especially in the context of home visits and community outreach. It also strengthens the student’s understanding of nursing responsibilities in real-life community settings. 📘 Key Topics Covered in the Presentation: Introduction to family health care: needs, principles, and objectives Assessment of health needs of individuals, families, and groups Observation and documentation during home visits and field assessments Identifying risk factors: environmental, behavioral, genetic, and social Conducting growth and development monitoring in infants and children Recording and observing: Milestones of development Menstrual health and reproductive cycle Temperature, blood pressure, and vital signs General physical appearance and personal hygiene Social assessment: understanding family dynamics, occupation, income, living conditions Health education and counseling for individuals and families Guidelines for early detection and referral of communicable and non-communicable diseases Maintenance of family health records and individual health cards Assisting families with: Maternal and child care Elderly and chronic disease management Hygiene and nutrition guidance Utilization of community resources – referral linkages, support services, and local health programs Role of nurse in coordinating care, advocating for vulnerable individuals, and empowering families Promoting self-care and family participation in disease prevention and health maintenance This presentation is highly useful for: Nursing students preparing for internal exams, university theory papers, or community postings Health educators conducting family teaching sessions Students conducting fieldwork and project work during community postings Public health nurses and outreach workers dealing with preventive, promotive, and rehabilitative care It’s structured in a step-by-step format, featuring tables, case examples, and simplified explanations tailored for easy understanding and classroom delivery.

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lecture#1 probability distribution .pptx

1. (MT-503) LECTURE NO.1 APPLIED STATISTICS

2. 1-2 REFERENCE BOOKS  ELEMENTARY STATISTICS BY ALAN G. BLUMAN (8TH EDITION).  PROBABILITY AND STATISTICS FOR ENGINEERS & SCIENTISTS BY WALPOLE & MYERS YE. (9TH EDITION).  APPLIED STATISTICS & PROBABILITY FOR ENGINEERS, BY Douglas C. Montgomery , George C. Runger.

4. 4 1. Define the terms probability distribution and random variable. 2. Distinguish between discrete and continuous probability distributions. 3. Calculate the mean, variance, and standard deviation of a discrete probability distribution. 4. Describe the characteristics of and compute probabilities using the binomial probability distribution. 5. Describe the characteristics of and compute probabilities using the Poisson probability distribution 6. Describe the characteristics of and compute probabilities using the –ve binomial and GOALS

5. What is a Probability Distribution? Experiment: Toss a coin three times. Observe the number of heads. The possible results are: zero heads, one head, two heads, and three heads. What is the probability distribution for the number of heads? 5

6. Probability Distribution of Number of Heads Observed in 3 Tosses of a Coin 6

7. Characteristics of a Probability Distribution 7 1. The probability of a particular outcome is between 0 and 1 inclusive. 2. The outcomes are mutually exclusive events. 3. The list is exhaustive. The sum of the probabilities of the

8. Random Variables Random variable :A real valued function define on sample is called random variable.. 8

9. Types of Random Variables 9  Discrete Random Variable can assume only certain clearly separated values. It is usually the result of counting something  Continuous Random Variable can assume an infinite number of values within a given range. It is usually the result of some type of measurement

10. Discrete Random Variables - Examples The number of students in a class. The number of children in a family. The number of cars entering a carwash in a hour. Number of home mortgages approved by Coastal Federal Bank last week. 10

11. Continuous Random Variables - Examples 11  The length of each song on the latest Tim McGraw album.  The weight of each student in this class.  The temperature outside as you are reading this book.  The amount of money earned by each of the more than 750 players currently on Major League Baseball team rosters.

12. Prob. Mass function (pmf):  f(x) = P(X=x) 12

13. The Mean of a discrete Probability Distribution Mean •The mean is a typical value used to represent the central location of a probability distribution. •The mean of a probability distribution is also referred to as its expected value. 13

14. The Variance, and Standard Deviation of a Discrete Probability Distribution 14

15. Mean, Variance, and Standard Deviation of a Discrete Probability Distribution - Example John Ragsdale sells new cars for Pelican Ford. John usually sells the largest number of cars on Saturday. He has developed the following probability distribution for the number of cars he expects to sell on a particular Saturday. 15

16. Mean of a Discrete Probability Distribution - Example 16

17. Variance and Standard Deviation of a Discrete Probability Distribution - Example  1.290  1.135 17  2  

18. Example : 18

19. 19

20. End of lecture 1 20

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