A random variable X has the following probability distribution:

Values of X : −2 −1 0 1 2 3

P (X) : 0.1 k 0.2 2k 0.3 k

Find the value of k.

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Solution

We know that the sum of probabilities in a probability distribution is always 1.

∴ P (X = $-$ 2) + P (X = $-$ 1) + P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1

$\Rightarrow 0.1 + k + 0.2 + 2 k + 0.3 + k = 1 \Rightarrow 4 k + 0.6 = 1 \Rightarrow k = \frac{0.4}{4} = 0.1$

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