Respuesta :
Answer:
Mean = 1.6
Variance = 0.84
Standard deviation = 0.916
Step-by-step explanation:
We are given the following probability distribution below;
X P(X) [tex]X \times P(X)[/tex] [tex]X^{2} \times P(X)[/tex]
0 0.1 0 0
1 0.4 0.4 0.4
2 0.3 0.6 1.2
3 0.2 0.6 1.8
Total 1.6 3.4
Now, the mean of the probability distribution is given by;
Mean, E(X) = [tex]\sum X \times P(X)[/tex] = 1.6
Also, the variance of the probability distribution is given by;
Variance, V(X) = [tex]\sum X^{2} \times P(X) - (\sum X \times P(X))^{2}[/tex]
= [tex]3.4 - (1.6)^{2}[/tex]
= 3.4 - 2.56 = 0.84
And the standard deviation of the probability distribution is given by;
Standard deviation, S.D. (X) = [tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{0.84}[/tex] = 0.916.
