The median of the normal distribution with mean and variance \(\mu\) and \(\sigma^2\) is:
\(\mu\)
For a normal distribution, the median equals the mean \(\mu\) due to symmetry. The median is the central value where 50% of the data lies on either side, coinciding with \(\mu\) in symmetric distributions like the normal curve.
Important Questions from Mean and Variance of Random variables
A continuous random variable x has a probability density function \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {6x\left( {1 - x} \right),}&{0 < x \le 1}\\ {0,}&{otherwise} \end{array}} \right.\) Then the variance of x is:
X is a non-negative integer valued random variable with
\( P(X = x) =\left\{ \begin{matrix} \dfrac {x+1}{2^{(x+2)}} & x = 0, 1, 2... \\\ 0 & \rm{otherwise} \end{matrix} \right.\)
Then, mean and variance of X are respectively
A random variable X has the distribution law as given below:
X
1
2
3
P(X = x)
0.3
0.4
0.3
The variance of the distribution is:
