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Model Institute of Engineering & Technology

Course Name –Engineering Mathematics-II

Course Code – BSC-201

Lecture No – 2

Topic – Binomial and Poisson Probability Distribution

Date –

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COURSE OUTCOMES

Course Outcomes	Description	Mapping with Program Outcomes and Program Specific Outcomes
CO1	To understand probability and random variables and various discrete and continuous probability distributions and their properties	1, 2, 4, 12
CO2	Calculate probabilities, and derive the marginal and conditional distributions of Bivariate random variables	1, 2, 4, 12
CO3	Analyse statistical data using measures of central tendency, dispersion and location	1, 2, 3, 5
CO4	Understand and discuss the issues surrounding sampling and significance	1,2, 3, 5
CO5	Develop analytical skills in structuring and interpreting the business problems statistically	1, 2, 5

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Course Outcome 1 - Delivery Plan

Course Outcomes	Topics	Blooms Taxonomy
CO1	To understand probability and random variables and various discrete and continuous probability distributions and their properties	Understanding

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Lesson Outcomes

Students will be able to:

Use binomial and Poisson distributions to model and analyze data from various fields, such as quality control, public health, and business.

Key Vocabulary:

Binomial Distribution

Poisson Distribution

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Assessment and Evaluation Plan

Assessment Tools

Quiz

Evaluation

SNAP Test

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PROBABILITY

Random Variables and Probability Distributions

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Random variable

The mathematical rule (or function) that assigns a given numerical value to each possible outcome of an experiment in the sample space of interest.

2 Types:

Discrete random variables
Continuous random variables

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The Binomial Distribution�Bernoulli Random Variables

Imagine a simple trial with only two possible outcomes:

Success (S)
Failure (F)

Examples

Toss of a coin (heads or tails)
Sex of a newborn (male or female)
Survival of an organism in a region (live or die)

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The Binomial Distribution�Overview

Suppose that the probability of success is p

What is the probability of failure?

q = 1 – p

Examples

Toss of a coin (S = head): p = 0.5 ⇒ q = 0.5
Roll of a die (S = 1): p = 0.1667 ⇒ q = 0.8333
Fertility of a chicken egg (S = fertile): p = 0.8 ⇒ q = 0.2

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The Binomial Distribution�Overview

Imagine that a trial is repeated n times
Examples:

A coin is tossed 5 times
A die is rolled 25 times
50 chicken eggs are examined

ASSUMPTIONS:

p is constant from trial to trial
the trials are statistically independent of each other

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CONDITIONAL PROBABILITY

Sample Problem 1: Black and white chips are placed in a box. Jack selects two chips without replacing the first one. If the probability of selecting a black chip and white chip is 30/67, and the probability of selecting a white chip on the first draw is 6/11, find the probability of selecting a black chip on the second draw, given that the first chip is white.

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CONDITIONAL PROBABILITY

Sample Problem 2: 9 red balls and 3 green marbles are place in a bag. Find the probability of randomly selecting a red marble on the first draw and a green marble on the second draw.

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CONDITIONAL PROBABILITY

Sample Problem 2: 9 red balls and 3 green marbles are place in a bag. Find the probability of randomly selecting a red marble on the first draw and a green marble on the second draw.

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CONDITIONAL PROBABILITY

Sample Problem 3: The probability Nathan buys butter is 0.10, and the probability that he buys bread and butter is 0.20. Find the probability that he will buy butter, given that he already bought bread.

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CONDITIONAL PROBABILITY

Sample Problem 3: The probability Nathan buys butter is 0.10, and the probability that he buys bread and butter is 0.20. Find the probability that he will buy butter, given that he already bought bread.