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

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMean and variance of a random variable2 Marks
Question
A random variable has the following probability distribution:
X = Xi 1 2 3 4
P(X = Xi) k 2k 3k 4k
Write the value of $\text{P}(\text{X}\geq3).$
✓

Answer

Here,

X = Xi 1 2 3 4
P(X = Xi) k 2k 3k 4k
Since, $\sum\text{P}(\text{X})=1$

⇒ P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1

⇒ k + 2k + 3k + 4k =1

⇒ 10k = 1

$\Rightarrow\text{k}=\frac{1}{10}$

$\text{P}(\text{X}\geq3)$

= P(X = 3) + P(X = 4)

= 3k + 4k

= 7k

$=\frac{1}{10}$

$\text{P}(\text{X}\geq3)=\frac{7}{10}$

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