Respuesta :
Answer:
E(x)=0.15
V(x)=0.3075
S(x)=0.5545
Step-by-step explanation:
The mean of a discrete variable is calculated as:
[tex]E(x)=x_1*p(x_1)+x_2*p(x_2)+...+x_n*p(n)[/tex]
where [tex]x_1,x_2,...,x_n[/tex] are the values that the variable can take and [tex]p(x_1),p(x_2),...,p(x_n)[/tex] are their respective probabilities.
So, if we call x the number of defective transistors in cartons, we can calculate the mean E(x) as:
[tex]E(x)=(0*0.92)+(1*0.03)+(2*0.03)+(3*0.02)=0.15[/tex]
Because there are 0 defective transistor with a probability of 0.92, 1 defective transistor with a probability of 0.03, 2 defective transistors with a probability of 0.03 and 3 defective transistors with a probability of 0.01.
At the same way, the variance V(x) is calculated as:
[tex]V(x)=E(x^2)-(E(x))^2[/tex]
Where [tex]E(x^2)=x_1^2*p(x_1)+x_2^2*p(x_2)+...+x_n^2*p(n)[/tex]
So, the variance V(x) is equal to:
[tex]E(x^2)=(0^2*0.92)+(1^2*0.03)+(2^2*0.03)+(3^2*0.02)=0.33\\V(x)=0.33-(0.15)^2\\V(x)=0.3075[/tex]
Finally, the standard deviation is calculated as:
[tex]S(x)=\sqrt{V(x)} \\S(x)=\sqrt{0.3075} \\S(x)=0.5545[/tex]
Answer:
mean = 0.15
variance = 0.3075
standard deviation = 0.5707
Step-by-step explanation:
- See the attachment an fill in the cells with "bold" marked columns.
- Where mean = E(X)
E(X) = Sum ( Xi*P(Xi) )
= 0 + 0.03 + 0.06 + 0.06
= 0.15
- The variance = Var (X)
Var (X) = Sum ( X2*P(X) ) - E(X)^2
= (0 + 0.03 + 0.12 + 0.18) - 0.15^2
= 0.3075
- The standard deviation = S(X)
S(X) = √Var(X) = √0.3075 = 0.5707
