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:
0.6
The mean is \(E[X]=1(0.3)+2(0.4)+3(0.3)=2\). Also \(E[X^2]=0.3+1.6+2.7=4.6\). Thus \(\operatorname{Var}(X)=4.6-2^2=0.6\).
Important Questions from Mean and Variance of Random variables
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
In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes is respectively given by
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:
Out of 100 numbers, 20 are 4's, 40 are 5's, 30 are 6's, and the remaining are 7's. The arithmetic mean of the numbers is:
The median of the normal distribution with mean and variance \(\mu\) and \(\sigma^2\) is:
