Respuesta :
Answer:
The standard deviation of given probability distribution is 0.767.
Step-by-step explanation:
We are given the following information in the question:
X: 0 1 2 3 4
P(x): 0.4521 0.3970 0.1307 0.0191 0.0010
Formula:
[tex]\text{Mean} = \sum X.P(x)\\= 0(0.4521) + 1(0.3970) + 2(0.1307) + 3(0.0191) + 4(0.0010)\\= 0.7197[/tex]
[tex]\mu = 0.7197[/tex]
Formula:
[tex]\text{Variance} = \sum (X-\mu)^2E(x)\\= (0-0.7197)^2(0.4521)+(1-0.7197)^2(0.3970)+(2-0.7197)^2(0.1307)+(3-0.7197)^2(0.0191)+(4-0.7197)^2(0.0010) \\=0.587 [/tex]
[tex]\text{Standard Deviation} = \sqrt{\text{Variance}}\\= \sqrt{0.587} = 0.767[/tex]
The standard deviation of given probability distribution is 0.767.
