In the following table, x is the discrete random variable and p(x) is the probability density function. The standard deviation of x is:| x | 1 | 2 | 3 - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 52026Mathematics

2 attempts50% success rate1 mark

In the following table, x is the discrete random variable and p (x) is the probability density function. The standard deviation of x is:| x | 1 | 2 | 3 | 4 ||---|---|---|---|---|| p (x) | 0.2 | 0.4 | 0.3 | 0.1 |

Solution & Step-by-step Explanation

Step 1: Calculate Mean E [X] = \sum x p (x) . E [X] = (1 \times 0.2) + (2 \times 0.4) + (3 \times 0.3) + (4 \times 0.1) = 0.2 + 0.8 + 0.9 + 0.4 = 2.3 Step 2: Calculate E [X^{2}] = \sum x^{2} p (x) . E [X^{2}] = (1^{2} \times 0.2) + (2^{2} \times 0.4) + (3^{2} \times 0.3) + (4^{2} \times 0.1) E [X^{2}] = (1 \times 0.2) + (4 \times 0.4) + (9 \times 0.3) + (16 \times 0.1) = 0.2 + 1.6 + 2.7 + 1.6 = 6.1 Step 3: Calculate Variance Va r (X) = E [X^{2}] - (E [X])^{2} . Va r (X) = 6.1 - (2.3)^{2} = 6.1 - 5.29 = 0.81 Step 4: Standard Deviation σ = Va r (X) = 0.81 = 0.9 .

Try it yourself before checking the explanation above.

In the following table, x is the discrete random variable and p (x) is the probability density function. The standard deviation of x is:| x | 1 | 2 | 3 | 4 ||---|---|---|---|---|| p (x) | 0.2 | 0.4 | 0.3 | 0.1 |

0.3

0.5

0.7

0.9

Practice with timed mock tests and track your performance across Mathematics.