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junior college 2 | H2 Maths
2 Answers Below
Anyone can contribute an answer, even non-tutors.
Can anyone please help? Very much appreciated.
Date Posted: 4 years ago
Views: 358
Non-negative integers means 0,1,2,3,...
P(X = x) = k(4⁻ˣ)
When x = 0, we have k(4⁻⁰) = k(1/4⁰) = k(1)
= k
When x = 1, we have k(4⁻¹) = k(1/4¹) = k/4
When x = 2, we have k(4⁻²) = k(1/4²) = k/16
We basically have a geometric series with first term k and common ratio ¼
Since |¼| < 1 , the series converges and we can have a sum to infinity.
Since the total probability is 1, the sum of all these probabilities should add up to 1.
i.e S∞ = 1
Using the formula S∞ = a/(1 - r),
k/(1 - ¼) = 1
k = ¾
P(X = x) = k(4⁻ˣ)
When x = 0, we have k(4⁻⁰) = k(1/4⁰) = k(1)
= k
When x = 1, we have k(4⁻¹) = k(1/4¹) = k/4
When x = 2, we have k(4⁻²) = k(1/4²) = k/16
We basically have a geometric series with first term k and common ratio ¼
Since |¼| < 1 , the series converges and we can have a sum to infinity.
Since the total probability is 1, the sum of all these probabilities should add up to 1.
i.e S∞ = 1
Using the formula S∞ = a/(1 - r),
k/(1 - ¼) = 1
k = ¾
Thank you for the very detail explaination. Really appreciated it.
Welcome
See 2 Answers
Actually no need to separate the 4⁻⁰ out. The GP can start from it.
Answered in comments.
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