Distribusi Binomial • Part 6: Contoh Soal Distribusi Peluang Variabel Acak Diskrit (3)

Summary

In this video from 'Jendela Sains,' the topic of binomial distribution is explored through a step-by-step example. The problem involves drawing two balls from a box containing 5 red and 3 blue balls. The video explains how to calculate the probability distribution and cumulative distribution for the number of red balls drawn. The presenter walks through the necessary calculations, covering combination formulas and how to fill in the probability tables. The video provides a clear breakdown of the solution, offering insights into probability theory and helping viewers grasp binomial distribution concepts.

Takeaways

• 😀 The video discusses the binomial distribution and the cumulative probability distribution for discrete random variables.
• 😀 The example involves a box containing 5 red balls and 3 blue balls, and two balls are drawn randomly at once.
• 😀 The random variable X represents the number of red balls drawn.
• 😀 There are three possible outcomes for the draw: two blue balls, one blue ball and one red ball, or two red balls.
• 😀 If two blue balls are drawn, X = 0 because no red balls are taken.
• 😀 If one blue ball and one red ball are drawn, X = 1 because one red ball is taken.
• 😀 If two red balls are drawn, X = 2 because both balls are red.
• 😀 The probability distribution (f(x)) is calculated using combinations (nCr) for each outcome.
• 😀 For X = 0 (two blue balls), the probability is 3/28.
• 😀 For X = 1 (one red and one blue ball), the probability is 15/28.
• 😀 For X = 2 (two red balls), the probability is 10/28, which simplifies to 5/14.
• 😀 The cumulative distribution (F(x)) is calculated by summing the probabilities up to the given value of X: F(0) = 3/28, F(1) = 18/28 (or 9/14), and F(2) = 1.

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