Answer:
0.78
Step-by-step explanation:
We have the next probability distribution:
X P(X)
0 0.2
1 0.3
2 0.5
As we can see when we add all the probabilites the result is 1. Now calculating the mean we have:
[tex]mean=\mu=(0\times0.2)+(1\times 0.3)+(2\times 0.5)=0+0.3+1=1.3[/tex]
The standard deviation is:
[tex]\sigma=\sqrt{\sum(x-\mu)^{2}(P(x))}[/tex]
Then using the data that we have:
[tex]\sigma=\sqrt{\sum(x-\mu)^{2}(P(x))}\\\sigma=\sqrt{(0-1.3)^{2}(0.2)+(1-1.3)^{2}(0.3)+(2-1.3)^{2}(0.5)}\\\\\sigma=\sqrt{(-1.3)^{2}(0.2)+(-0.3)^{2}(0.3)+(0.7)^{2}(0.5)}\\\\\sigma=\sqrt{(1.69)(0.2)+(0.09)(0.3)+(0.49)(0.5)}\\\\\sigma=\sqrt{0.338+0.027+0.245}\\\\\sigma=\sqrt{0.61}\\\\\sigma=0.78\\[/tex]
Then the standard deviation is 0.78
