Maths · Probability: Probability of an event, addition and multiplication theorems of probability
The variance of the random variable whose probability distribution is given by :
The variance of the random variable \( x \) whose probability distribution is given by \( \boldsymbol{X}=\boldsymbol{x}_{i}: \quad-1 \quad, \boldsymbol{0}, \quad+1 \) \( \boldsymbol{p}\left(\boldsymbol{X}=\boldsymbol{x}_{i}\right): \mathbf{0 . 4}, \mathbf{0 . 2}, \quad \mathbf{0 . 4} \) is
- A. 0.4
- B. 0.6
- C. 0 .8 \)
- D. 1.0
Step-by-step solution
Mean μ = (-1)(0.4) + (0)(0.2) + (1)(0.4) = 0. Variance = E[X^2] - μ^2. E[X^2] = (1)(0.4) + (0)(0.2) + (1)(0.4) = 0.8. Thus variance = 0.8.
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