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Mean and variance of a random variable — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMean and variance of a random variable2 Marks
Question
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.
✓

Answer

Here,
Values of X: -2 -1 0 1 2 3
P(X) 0.1 k 0.2 2k 0.3 k
We know that,
P(-2) + P(-1) + P(0) + P(1) + P(2) + P(3) = 1
⇒ 0.1 + k + 0.2 + 2k + 0.3 + k = 1
⇒ 4k + 0.6 = 1
⇒ 4k = 1 - 0.6
⇒ 4k = 0.4
$\Rightarrow\text{k}=\frac{0.4}{4}$
$\Rightarrow\text{k}=\frac{1}{10}$
$\Rightarrow\text{k}=0.1$

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