Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Probability Distributions

Question:

Find the mean, variance and standard deviation of the probability distribution:

X

2

3

4

P(X)

0.2

0.5

0.3

Options:

Mean = 3.1, Variance = 0.49, Standard deviation = 0.7

Mean = 3.1, Variance = 0.29, Standard deviation = 0.54

Mean = 3, Variance = 0.5, Standard deviation = 0.5

Mean = 3.5, Variance = 1.25, Standard deviation = 1.12

Correct Answer:

Mean = 3.1, Variance = 0.49, Standard deviation = 0.7

Explanation:

The correct answer is Option (1) → Mean = 3.1, Variance = 0.49, Standard deviation = 0.7

We construct the following table:

$x_i$

$p_i$

$p_ix_i$

$p_i{x_1}^2$

2

0.2

0.4

0.8

3

0.5

1.5

4.5

4

0.3

1.2

4.8

Total

 

3.1

10.1

Mean = $μ = 3.1$

Variance = $Σp_i{x_i}^2- μ^2 = 10.1 - (3.1)^2 = 10.1-9.61 = 0.49$

Standard deviation = $\sqrt{0.49} = 0.7$