In: Statistics and Probability
Calculate the standard deviation σ of X for the probability distribution. (Round your answer to two decimal places.) σ = x 1 2 3 4 P(X = x) 0.2 0.3 0.4 0.1
Solution :
Mean =
=
X * P(X)
= 1 *0.2 + 2 * 0.3 + 3 * 0.4 + 4 * 0.1
= ( 0.2+ 0.6+ 1.2+ 0.4)
= 2.4
Standard deviation =
=X
2 * P(X) -
2
= [
12 *0.2 + 22 * 0.3 + 32 * 0.4 + 42 * 0.1]-2.42
=
[( 0.2+ 1.2 + 3.6 +1.6 ) )]-5.76
=6.6-5.76
=0.84
=0.92
Standard deviation =
=0.92