Can anyone tell me if this is correct?
Given the following probability distribution, calculate the mean, variance, and standard deviation.
x P(x)
1 0.125
2 0.236
3 0.543
4 0.096
The requirements have been met for a probability distribution.
µ = Sum x * P (x)$
µ = Sum [1 * 0.125 + 2* 0.236 + 3*0.543 + 4 * 0.096] = [0.125 + 0.472 + 1.629 + 0.384]
µ = 2.6 (rounded)
variance: s^2 = Sum [x^2 * P (x)] - µ^2 =
Sum [(x- µ)^2 * P(x)] =
(1- 2.61)^2 * 0.125 = (-1.61)^2 * 0.125 = 2.592 * 0.125 = 0.324
(2- 2.61)^2 * 0.236 = (-0.61)^2 * 0.236 = 0.372 * 0.236 = 0.087
(3-2.61)^2 * 0.0543 = (0.39)^2 *0.0543 = 0.152 * 0.0543 = 0.008
(4 - 2.61)^2 * 0.096 = (1.39)^2 * 0.096 = 1.932 * 0.096 = 0.185
Sum = 0.324 +0.087+0.008+0.185 = 0.604 = 0.6 (Rounded)
Standard deviation: s = square root of variance
Standard deviation = 0.777 = 0.8 (rounded)