The variance of degenerate random variable is:
0
A degenerate random variable \(X\) takes a single value \(c\) with probability 1, so \(E[X]=c\) and
\[\text{Var}(X) = E[(X-c)^2] = E[0] = 0\]
There is no dispersion because the variable never deviates from its mean. Hence the variance is 0.
Similar Questions
The fourth central moment of a mesokurtic distribution is 243. Its standard deviation is:
The standard deviation of the first 10 natural numbers is 3.028. What will be the standard deviation of the first 20 natural numbers?
If n 1= 10 and n 2= 5 are the sizes, \(\rm\bar{x}_1\) = 7 and \(\rm\bar{x}_2\) = 4 are the means and σ 1= 1 and σ 2= 1 are the standard deviations of two series of data. If combined mean \(\rm\bar{x}\) = 6, then the variance of the combined series with size n 1+ n 2is equal to:
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Among these options, which one is NOT an example of relative measure of dispersion?
Important Questions from Variance and Standard Deviation
Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?
When sampling is done without replacement then standard error of mean is:
Consider a population that is finite, and sampling is with replacement. If the variance of the population is 2176.8 with a sample size of 16, then the variance of the sampling distribution of means is:
If \(\rm \displaystyle \sum_{i = 1}^{10}x_i = 110\) and \(\rm \displaystyle \sum_{i = 1}^{10}x_i^2 = 1540\) then what is the variance?
The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2 = 10000, then what is the value of n?
