🎯 Key Takeaways for quick navigation: 00:13 🔄 *Format Change and Introduction to Multiple Random Variables* - Introduction to a new slide format symbolizing a change in the course. - Week 3 focus on dealing with multiple random variables in a probability space. - Explanation of the importance and complexity of handling distributions involving multiple random variables. 02:02 🎲 *Example: Tossing a Fair Coin Multiple Times* - Definition of three random variables (X1, X2, X3) representing outcomes of multiple coin tosses. - Use of indicator functions to represent outcomes (Heads/Tails) of individual tosses. - Observation of independence between events defined with different random variables. 06:22 🔢 *Example: Two-Digit Lottery Number Selection* - Introduction to a more complex scenario involving a two-digit lottery number. - Definition of two random variables (X and Y) representing units place and remainder when divided by 4. - Demonstration that both X and Y are uniformly distributed in their respective ranges. 10:45 🔄 *Independence and Dependence: Impact of One Variable on Another* - Explanation of how events defined with X and Y may not be independent in the lottery example. - Insight into the influence of one random variable on another in specific scenarios. - Emphasis on the practical importance of understanding dependencies when modeling complex experiments. 14:25 🏏 *Application: IPL Powerplay Modeling with Two Random Variables* - Introduction of two random variables (X and Y) in the context of IPL powerplay overs. - Discussion on how understanding relationships between X and Y can aid in modeling cricket over outcomes. - Illustration of how these relationships can be valuable when interpreting and building models for complex experiments. 15:43 📊 *Focus on Joint PMFs and Introduction to Three Types* - Introduction to joint PMFs, marginal PMFs, and conditional PMFs for two discrete random variables. - Emphasis on the importance of understanding and manipulating these PMFs. - Announcement of the upcoming section's focus on defining and exploring joint PMFs. 17:11 🎯 *Joint PMF of X and Y* - The joint PMF (Probability Mass Function) of two discrete random variables, X and Y, is denoted as fxy. - fxy is a function defined on the Cartesian product of the ranges of X and Y, assigning a probability value to each pair (t1, t2) from these ranges. 19:01 📊 *Representing Joint PMF* - Joint PMF can be represented as a table or matrix, with rows corresponding to the values of X and columns to the values of Y. - Notation: Instead of "and," a comma is used, e.g., X=t1, Y=t2, to simplify the representation of joint PMF. 20:50 🎲 *Example: Tossing a Fair Coin Twice* - Demonstrates the joint PMF calculation for the scenario of tossing a fair coin twice with random variables X1 and X2. - Utilizes independence of events, showing that the joint PMF is calculated by multiplying individual probabilities. 23:30 🔄 *Properties of Joint PMF* - Two fundamental properties of joint PMF: Each entry is between 0 and 1, and the sum of all entries equals 1. - The sum being 1 indicates that the joint PMF accounts for all possible outcomes of X and Y. 25:07 🔢 *Example: Random 2-Digit Number* - Examines the joint PMF for a scenario involving a random 2-digit number, where X is the units place, and Y is the remainder when divided by 4. - Demonstrates the calculation of specific joint PMF values, considering the conditions of X and Y.
Guys I need an reply urgently please help me , so I applied for bsc in data science on August 30th which is yesterday. Now I saw these classes on TH-cam. Has the 4 weeks training already started ? When does 4 weeks training for exam start for me ? I kindly request anyone to answer me pleaseeee.
🎯 Key Takeaways for quick navigation:
00:13 🔄 *Format Change and Introduction to Multiple Random Variables*
- Introduction to a new slide format symbolizing a change in the course.
- Week 3 focus on dealing with multiple random variables in a probability space.
- Explanation of the importance and complexity of handling distributions involving multiple random variables.
02:02 🎲 *Example: Tossing a Fair Coin Multiple Times*
- Definition of three random variables (X1, X2, X3) representing outcomes of multiple coin tosses.
- Use of indicator functions to represent outcomes (Heads/Tails) of individual tosses.
- Observation of independence between events defined with different random variables.
06:22 🔢 *Example: Two-Digit Lottery Number Selection*
- Introduction to a more complex scenario involving a two-digit lottery number.
- Definition of two random variables (X and Y) representing units place and remainder when divided by 4.
- Demonstration that both X and Y are uniformly distributed in their respective ranges.
10:45 🔄 *Independence and Dependence: Impact of One Variable on Another*
- Explanation of how events defined with X and Y may not be independent in the lottery example.
- Insight into the influence of one random variable on another in specific scenarios.
- Emphasis on the practical importance of understanding dependencies when modeling complex experiments.
14:25 🏏 *Application: IPL Powerplay Modeling with Two Random Variables*
- Introduction of two random variables (X and Y) in the context of IPL powerplay overs.
- Discussion on how understanding relationships between X and Y can aid in modeling cricket over outcomes.
- Illustration of how these relationships can be valuable when interpreting and building models for complex experiments.
15:43 📊 *Focus on Joint PMFs and Introduction to Three Types*
- Introduction to joint PMFs, marginal PMFs, and conditional PMFs for two discrete random variables.
- Emphasis on the importance of understanding and manipulating these PMFs.
- Announcement of the upcoming section's focus on defining and exploring joint PMFs.
17:11 🎯 *Joint PMF of X and Y*
- The joint PMF (Probability Mass Function) of two discrete random variables, X and Y, is denoted as fxy.
- fxy is a function defined on the Cartesian product of the ranges of X and Y, assigning a probability value to each pair (t1, t2) from these ranges.
19:01 📊 *Representing Joint PMF*
- Joint PMF can be represented as a table or matrix, with rows corresponding to the values of X and columns to the values of Y.
- Notation: Instead of "and," a comma is used, e.g., X=t1, Y=t2, to simplify the representation of joint PMF.
20:50 🎲 *Example: Tossing a Fair Coin Twice*
- Demonstrates the joint PMF calculation for the scenario of tossing a fair coin twice with random variables X1 and X2.
- Utilizes independence of events, showing that the joint PMF is calculated by multiplying individual probabilities.
23:30 🔄 *Properties of Joint PMF*
- Two fundamental properties of joint PMF: Each entry is between 0 and 1, and the sum of all entries equals 1.
- The sum being 1 indicates that the joint PMF accounts for all possible outcomes of X and Y.
25:07 🔢 *Example: Random 2-Digit Number*
- Examines the joint PMF for a scenario involving a random 2-digit number, where X is the units place, and Y is the remainder when divided by 4.
- Demonstrates the calculation of specific joint PMF values, considering the conditions of X and Y.
i just can't understnd anythign
I know about this yesterday but unfortunately you didn't mentioned the last date clearly on website.kindly extend the admission date for some days
Seems like there is going to be a little change this term...I remember seeing basic probability recap from stats 1 in the initial weeks of stats 2.
thats week 0 now
Thank You Sir
Sir how can I enroll in this course? application ended on 30 August.
Please Help me
next term in january
I passed 12th this year & I want to pursue online bsc from iitm.Please sir open your application window.January will be late for me.
Guys I need an reply urgently please help me , so I applied for bsc in data science on August 30th which is yesterday. Now I saw these classes on TH-cam. Has the 4 weeks training already started ?
When does 4 weeks training for exam start for me ?
I kindly request anyone to answer me pleaseeee.
@@sushmap9603 It starts on 6th September.
@@autodidact3070 thank you so much
sir is this for qualifier exam
nope
lecture is from stat 2
28:56 marginal *pmf 😅
Where to get the slides