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:
5.3
To calculate the arithmetic mean, we use the formula:
Mean = (Σ(xi * fi)) / N
Where xi is the value, fi is the frequency, and N is the total number of observations. Substituting the values:
Mean = [(20 * 4) + (40 * 5) + (30 * 6) + (10 * 7)] / 100 = 530 / 100 = 5.3
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:
