: Random Variable, Discrete Random variable, Continuous random variable, Probability Distribution of Discrete Random variable, Mathematical Expectations and variance of a discrete random variable.
A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution. Suppose we flip a coin two times and count the number of heads (successes).
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
Topic Covered in this video:
1. What is Discrete Probability Distribution
2. Types of Theoretical Discrete Probability Distribution
3. Binomial Distribution
4. Properties of Binomial Distribution
5. Examples of Binomial distribution
6. Fitting of Binomial Distribution
7. Application of Binomial distribution
: Random Variable, Discrete Random variable, Continuous random variable, Probability Distribution of Discrete Random variable, Mathematical Expectations and variance of a discrete random variable.
A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution. Suppose we flip a coin two times and count the number of heads (successes).
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
Topic Covered in this video:
1. What is Discrete Probability Distribution
2. Types of Theoretical Discrete Probability Distribution
3. Binomial Distribution
4. Properties of Binomial Distribution
5. Examples of Binomial distribution
6. Fitting of Binomial Distribution
7. Application of Binomial distribution
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اگر آپ تعلیمی نیوز، رجسٹریشن، داخلہ، ڈیٹ شیٹ، رزلٹ، اسائنمنٹ،جابز اور باقی تمام اپ ڈیٹس اپنے موبائل پر فری حاصل کرنا چاہتے ہیں ۔تو نیچے دیے گئے واٹس ایپ نمبرکو اپنے موبائل میں سیو کرکے اپنا نام لکھ کر واٹس ایپ کر دیں۔ سٹیٹس روزانہ لازمی چیک کریں۔
نوٹ : اس کے علاوہ تمام یونیورسٹیز کے آن لائن داخلے بھجوانے اور جابز کے لیے آن لائن اپلائی کروانے کے لیے رابطہ کریں۔
This presentation is a part of Business analytics course.
Probability Distribution is a statistical function which links or lists all the possible outcomes a random variable can take, in any random process, with its corresponding probability of occurrence.
The PPT covered the distinguish between discrete and continuous distribution. Detailed explanation of the types of discrete distributions such as binomial distribution, Poisson distribution & Hyper-geometric distribution.
JEE Mathematics/ Lakshmikanta Satapathy/ Theory of probability part 10/ Bernoulli trials and Binomial distribution of probability of Bernoulli trials and probability function with example
Basic Concepts, Components of time series. The trend, Fitting of trend by least square method and moving average method, uses of time series in business.
Collection of primary and secondary data, classification. types of classification, frequency distribution, cumulative frequency distribution. Diagrammatic and graphical representation of data.
Definition- Problems for construction. Construction of price, quantity, value and cost of living index numbers, ideal index, tests and uses of index numbers.
Students’t distribution, small sample inference about population mean and the difference between two means. paired difference tests, inferences about population variance
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
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http://sandymillin.wordpress.com/iateflwebinar2024
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This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Probability Distribution:
A probability distribution describes the behavior of a random variable. Many times
the observations obtained from different random experiments have a general type of
behavior.
Therefore, the random variable(s) associated with these experiments have a general
type of probability distribution.
So it can be represented by a single formula. This type of single formula
about the behavior of a random variable is known as probability distribution.
3. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Discrete Probability Distribution:
The probability distribution of a discrete random variable that arise from some
statistical experiments is known as discrete probability distribution.
The following are some of the commonly discussed discrete distribution:
i. Uniform distribution
ii. Bernoulli distribution
iii.Binomial distribution
iv.Negative binomial distribution
v. Poisson distribution
vi.Geometric distribution
vii.Hypergeometric distribution
4. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Bernoulli Trial:
When in the trial of a random experiment each trial is independent and in each the
number of possible outcomes are dichotomous, then the trial are called Bernoulli trial.
In Bernoulli trial, the outcome are known as ‘Success’ and ‘Failure’ or having a certain
quality or absence of that quality.
Here, the probability of success is denoted by p and the probability of failure is denoted by
(1-P)= q. These probability remains constant from trial to trial.
5. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Examples of Bernoulli’s Trails are:
1) Toss of a coin (head or tail)
2) Throw of a die (even or odd number)
3) Performance of a student in an examination (pass or fail)
6. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Bernoulli Distribution:
If a random variable x can assume only two values, failure and a success with
probabilities 𝑃 𝑥 = 1 = 𝑝 and 𝑃 𝑥 = 0 = 1 − 𝑝.
Then the distribution of x might be termed as a Bernoulli distribution with parameter p.
The probability distribution of Bernoulli variate x can be written as,
𝑷 𝑿 = 𝒙; 𝒑 = 𝒑 𝒙
𝒒 𝟏−𝒙
; 𝒙 = 𝟎, 𝟏
= 𝟎 ; 𝑶𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
7. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Example:
When a coin is tossed either head or tail will appear. If we consider having a head as the
„Success‟ and „Failure‟ otherwise then this be termed as Bernoulli trial and its
distribution as Bernoulli distribution.
8. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Binomial Trial:
A binomial trial is the extension of Bernoulli trial. In a binomial experiment, the
trial is repeated several times. A binomial experiment should have the following properties:
i. The experiment consists of n repeated trials
ii. The trials are independent of each other
iii.The probability of success (failure) remains constant from trial to trial.
9. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
3.1.2 Binomial Distribution:
A random variable X is said to follow binomial distribution, if its probability mass
function is given by
Here, the two independent constants n and p are known as the „parameters‟ of the
distribution.
The distribution is completely determined if n and p are known. x refers the number of
successes.
Where, n = No. of trials
p = Probability of success
q = Probability of failure
10. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
3.1.3 Condition for Binomial Distribution:
We get the Binomial distribution under the following experimental conditions.
i. The number of trials ‘ n’ is finite.
ii. The trials are independent of each other.
iii. The probability of success ‘ p’ is constant for each trial.
iv. Each trial must result in a success or a failure.
The problems relating to tossing of coins or throwing of dice or drawing cards from a pack
of cards with replacement lead to binomial probability distribution.
11. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
3.1.4 Characteristics of Binomial Distribution:
1. Binomial distribution is a discrete distribution in which the random variable X
(the number of success) assumes the values 0,1, 2, ….n, where n is finite.
2. Mean = np, variance = npq and
clearly each of the probabilities is non-negative and sum of
all probabilities is 1 ( p < 1 , q < 1 and p + q =1, q = 1- p ).
13. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Comment on the following: “ The mean of a binomial distribution is 5 and its variance is 9”
The parameters of the binomial distribution are n and p
We have, mean = np = 5
Variance = npq = 9
Which is not admissible since q cannot exceed unity. Hence
the given statement is wrong.
14. Bipul Kumar Sarker, Lecturer (BBA Professional), HBUC
Example 2:
Eight coins are tossed simultaneously. Find the probability of getting at least six heads.
Solution:
Given that,
No. of trials, n = 8
The probability of getting a head, p =
1
2
The probability of getting a head, q = (1-p) =
1
2
Let, x be denoted the number of getting a head
16. Example 3:
Ten coins are tossed simultaneously. Find the probability of getting
i. At least seven heads
ii. Exactly seven heads
iii. At most seven heads
17. Solution: Given that,
No. of trials, n = 8
The probability of getting a head, p =
1
2
The probability of getting a head, q = (1-p) =
1
2
Let, x be denoted the number of getting a head
Therefore, the probability function,
𝑷 𝑿 = 𝒙; 𝒑 = 𝒏 𝑪 𝒙
𝒑 𝒙 𝒒(𝒏−𝒙) ; x = 0, 1, 2, 3, 4, …, 9, 10
18. i. Probability of getting at least seven heads is given by
ii. Probability of getting exactly 7 heads
19. iii. Probability of getting at most 7 heads
𝑷 𝑿 ≤ 7 = 𝑷 𝑿 = 0 + 𝑷 𝑿 = 1 + ⋯ … … . +𝑷 𝑿 = 7