For the random variable X with probability density function f(x) = (x3)25 ; x = 3, 4, 5, the variance of X is:

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SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. 225
  2. 25
  3. 45
  4. 425

Answer (Detailed Solution Below)

Option 4 : 425
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The correct answer is  4/25.

Key Points

  • The variance of a random variable X with probability density function f(x) is defined as the expected value of the squared deviation of X from its mean, and can be calculated as E[(XE[X])2].
  • To find the variance of X in this case, you would need to know the full form of f(x) and calculate E[X] and E[(XE[X])2].
  • Variance measures the spread or dispersion of a set of data or a random variable around its mean.
  • A smaller variance indicates that the data is clustered closely around the mean, while a larger variance indicates that the data is more spread out.
  • Variance is a important quantity in statistics and probability, and is used in many statistical models and hypothesis tests.
  • Variance is always non-negative and its square root, the standard deviation, is a commonly used measure of spread.

 Additional Information

  • Variance is a measure of the second moment or central moment about the mean of a set of data or a random variable.
  • The variance of a random variable is also related to the expected value (mean) of the squared deviation of the random variable from its mean.
  • The variance is an important quantity in the study of random variables, as it provides information about the distribution and spread of the data.
  • In some cases, the variance may not provide a complete picture of the spread of the data. In such cases, other measures such as the coefficient of variation or interquartile range may be used.
  • Variance is a key parameter in many statistical models, including regression analysis, analysis of variance (ANOVA), and others.
  • Understanding and being able to calculate the variance is a fundamental skill for anyone working in the field of statistics and data analysis.
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