ExamBro
ExamBro
TS EAMCET · Maths · Statistics

If \(m\) and \(\sigma^2\) are the mean and variance of the random variable \(X\), whose distribution is given by
Then

  1. A \(m=\sigma^2=2\)
  2. B \(m=1, \sigma^2=2\)
  3. C \(m=\sigma^2=1\)
  4. D \(m=2, \sigma^2=1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(m=\sigma^2=1\)

Step-by-step Solution

Detailed explanation

Given, distribution is \(\begin{aligned}\therefore Mean, m & =\sum_{i=1}^4 p_i x_i \\ & =0 \times \frac{1}{3}+1 \times \frac{1}{2}+2 \times 0+3 \times \frac{1}{6}\end{aligned}\) \(=0+\frac{1}{2}+0+\frac{1}{2}=1\) Variance, \(\sigma^2=\sum_{i=1}^4 p_i\left(x_i-m\right)^2\)…