Introduction to variance of discrete random variable:

The discrete random variables have the countable values for their probability. The variance value for the discrete random variable is calculated with the help of the mean. The random variables are said to discrete random variable when the sum of their probability is one. The online produces the link between the tutor and the students. With the help of the online the students clarify their doubts. This article contains the information about the discrete random variables in the probability theory and statistics.

Formula Used for Solve Online Discrete Random Variables:

The formulas used to determine variance for the discrete random variable are

Variance = `sum p(x) (x^2) - (sum x p(x)) ^2`

In this above mentioned formula the `(sum x p(x)) ^2` is the squared value of the mean in the statistics.

In the above formula x denotes the given set of discrete random values and p(x) denotes the probability value for the discrete random variables in the statistics.Having problem with what are exponents keep reading my upcoming posts, i will try to help you.

Examples for Solve Online Discrete Random Variables:

Example 1 to solve online discrete random variables:

Predict the mean, variance and standard deviation for the discrete random variables.

x	2	4	6	8	9
P(x)	0.23	0.21	0.30	0.11	0.15

Solution:

Mean = `sum x p(x)`

Mean = 2 (0.23) +4 (0.21) +6 (0.30) +8 (0.11) + 9(0.05)

Mean = 0.46+ 0.84 + 1.8 + 0.88 + 0.45

Mean = 4. 43

Variance = `sum p(x) (x^2) - (sum x p(x)) ^2`

Variance = ((0.23) (2) (2) + (0.21) (4) (4) + (0.30) (6) (6) + (0.11) (8) (8) + (0.15) (9) (9)) - (4.43)2

Variance = (0.92+ 3.36+ 10.8 + 7.04+ 12.15) - 19.6249

Variance = 34.27 -21.5296

Variance = 46.42

The variance for the discrete random variable is 46.42.

Example 2 to solve online discrete random variables:

Predict the mean, variance and standard deviation of discrete random variables.

x	10	20	-30	40	50
P(x)	0.22	0.12	0.25	0.05	0.36

Solution:

Mean = `sum x p(x)`

Mean = 10(0.22) +20(0.12) - 30(0.25) +40(0.05) + 50(0.36)

Mean = 2.2 +2.4 -7.5+ 2+ 18

Mean = 17.1

Variance = `sum p(x) (x^2) - (sum x p(x)) ^2`

Variance = ((0.22) (10) (10) + (0.12) (20) (20) + (0.25) (-30) (-30) + (0.05) (40) (40) + (0.36) (50) (50)) - (17.1)2

Variance = (22+48+ 225 + 80 +900) -292.41

Variance = 1275 - 292.41

Variance = 982.59

The variance for the discrete random variable is 982.59.