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📘 Probability Distributions – Important Solved Problems

In this video, we solve exam-focused problems on Random Variables, Probability Distributions, Mean & Variance, and Standard Deviation step by step. These are commonly asked in university exams and competitive tests.

🔢 Questions Covered in this Video:

Question 1 (00:20)
A coin is tossed twice. A random variable X represents the number of heads turning up. Find the probability distribution of X and also compute its mean and variance.

Question 2 (07:25)
A coin is tossed thrice. A random variable X represents the number of tails turning up. Find the probability distribution of X and also compute its mean and variance.

Question 3 (13:50)
A random experiment of tossing a die is performed. A random variable on this sample space is defined to be the sum of the numbers turning up on the die. Find the discrete probability distribution of X and compute the corresponding mean and standard deviation.

Question 4 (22:47)
From a sealed container containing a dozen apples, it was found that 3 apples are perished. Obtain the probability distribution of the number of perished apples when two apples are drawn at random, and also find the mean and variance of the distribution.

✨ What You’ll Learn in This Video:
✔ How to construct a probability distribution table
✔ How to calculate Mean, Variance, and Standard Deviation
✔ Step-by-step explanation with clear reasoning
✔ Useful for VTU, B.Sc., B.E., B.Tech., and competitive exams

📌 Make sure to watch till the end for complete clarity!

📘 Probability Distributions – VTU BCS301 Module 1

🎥 Full Playlist (Autoplay all problems)
   • Плейлист  

📌 Problems with Direct Links:

1️⃣ Coin & Die Problems –    • Probability Distribution | Example Problem...  

2️⃣ Discrete Distribution (Mean & Var) –    • Probability Distribution | Example Problem...  

3️⃣ Find k, Mean & Std Dev –    • Probability Distribution | Example Problem...  

4️⃣ Perished Apples Distribution –    • Probability Distribution | Example Problem...  

5️⃣ Probability Function (Find k & P(x)) –    • Probability Distribution | Example Problem...  

6️⃣ Distribution P(x)=kx (Mean & Var) –    • Probability Distribution | Example Problem...  

7️⃣ Binomial (Mean & Std Dev) –    • Binomial Distribution: Easy Proof of Mean ...  

8️⃣ Binomial (Coin Toss & Def Pens) –    • Binomial Distribution - Example Problem 1 ...  

9️⃣ Binomial (Def Lamps & Survival) –    • Binomial Distribution - Example Problem 2 ...  

🔟 Binomial (Telephone & Quiz) –    • Binomial Distribution - Example Problem 3 ...  

1️⃣1️⃣ Poisson (Defectives in Samples) –    • Binomial Distribution - Example Problem 4 ...  

1️⃣2️⃣ Poisson (Students Test) –    • Binomial Distribution - Example Problem 5 ...  

1️⃣3️⃣ Airline Seats & Families –    • Binomial Distribution - Example Problem 6 ...  

1️⃣4️⃣ Fitting Binomial (Dice & Coins) –    • Binomial Distribution - Example Problem 7 ...  

1️⃣5️⃣ Poisson (Mean & SD) –    • Mean and Variance of Poisson Distribution ...  

1️⃣6️⃣ Fit Poisson (Accidents Data) –    • Poisson Distribution | Fit Observed Data &...  

1️⃣7️⃣ Poisson (Blades & Fuses) –    • Poisson Distribution | Probability of Defe...  

1️⃣8️⃣ Poisson (Injection Reactions) –    • Poisson Distribution Example | Injection R...  

1️⃣9️⃣ PDF f(x)=(x/6)+c –    • Continuous Random Variable| Probability De...  

2️⃣0️⃣ PDF f(x)=kx² (0 to 3)–    • Continuous Random Variable | Probability D...  

2️⃣1️⃣ PDF f(x)=kx² [-3 to 3] –    • Continuous Random Variable | PDF | Find k ...  

2️⃣2️⃣ PDF f(x)=kx·e^(-x) –    • Continuous Random Variable | Probability D...  

2️⃣3️⃣ Exponential (Mean=3) –    • Probability Distributions | Exponential Di...  

2️⃣4️⃣ Exponential (Mean=5) –    • Probability Distributions | Exponential Pr...  

2️⃣5️⃣ Exponential (Calls) –    • Exponential Probability Distribution | Tel...  

2️⃣6️⃣ Exponential (Showers) –    • Exponential Distribution | Shower Duration...  

2️⃣7️⃣ Normal (Mean=30, SD=5) –    • Normal Distribution - Example Problem 1 | ...  

2️⃣8️⃣ Normal (1000 Students Marks) –    • Normal Distribution - Example Problem 2 | ...  

2️⃣9️⃣ Normal (Bulb Lifetime) –    • Normal Distribution - Example Problem 3 | ...  

3️⃣0️⃣ Normal (Find Mean & SD) –    • Normal Distribution - Example Problem 4 | ...  

3️⃣1️⃣ Normal (Exam Marks) –    • Normal Distribution - Example Problem 5 | ...  

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