Respuesta :
Answer:
[tex]\mu=0.4[/tex]
[tex]V=8.64[/tex]
[tex]\sigma=2.94[/tex]
Step-by-step explanation:
Given : The probability distribution of a random variable X.
To find : The mean, variance, and standard deviation of X.
Solution :
First we create the table as per requirements,
x P(x) xP(x) x² x²P(x)
4 0.3 1.2 16 4.8
2 0.1 0.2 4 0.4
0 0.3 0 0 0
-2 0.1 -0.2 4 0.4
-4 0.2 - 0.8 16 3.2
∑P(x)=1 ∑xP(x)=0.4 ∑x²P(x)=8.8
1) The mean of x is defined as
[tex]\mu=\sum xP(x)=0.4[/tex]
2) The variance of x is defined as
[tex]V=\sum x^2P(x)-(\sum xP(x))^2\\V=8.8-(0.4)^2\\V=8.8-0.16\\V=8.64[/tex]
3) The standard deviation of x is defined as
[tex]\sigma=\sqrt{V}\\\sigma=\sqrt{8.64}\\\sigma=2.94[/tex]
