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Solve the following problem : A random variable X has the following probability distribution. x 1 2 3 4 5 6 7 P(x) k 2k 2k 3k k2 2k2 7k2 + k Determine k - Mathematics and Statistics

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Sum

Solve the following problem :

A random variable X has the following probability distribution.

x 1 2 3 4 5 6 7
P(x) k 2k 2k 3k k2 2k2 7k2 + k

Determine k

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Solution

The table gives a probability distribution and therefore \[\sum\limits_{i=1}^{7} \text{P}_i\] = 1

∴ k + 2k + 2k + 3k + k2 + 2k2 + 7k2 + k = 1

∴ 10k2 + 9k – 1 = 0

∴ 10k2 + 10k – k – 1 = 0

∴ 10k(k + 1) – 1(k + 1) = 0

∴ (10k – 1) (k + 1) = 0

∴ k = `(1)/(10)` or k = – 1

But k cannot be negative

∴ k = `(1)/(10)`.

Concept: Random Variables and Its Probability Distributions
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