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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 variable1 Mark
Question
The probability distribution of a discrete random variable X is given below:

$\text{X}:$
$1$
$2$
$3$
$4$
$\text{P}(\text{X}):$
$\frac{1}{10}$
$\frac{1}{5}$
$\frac{3}{10}$
$\frac{2}{5}$

The value of E(X2) is:

  1. 3
  2. 5
  3. 7
  4. 10
✓

Answer

  1. 10

Solution:

$\text{X}$

$1$

$2$

$3$

$4$

 

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

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{3}{10}$

$\frac{2}{5}$

 

$\text{X}^2\text{P(X)}$

$\frac{1}{10}$

$\frac{4}{5}$

$\frac{27}{10}$

$\frac{32}{5}$

$\text{E}(\text{X}^2)=10$

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