Question

Let’s calculate the variance for the given data:

Calculate E(X):

𝐸
(
𝑋
)
=
(
3
∗
0.1
)
+
(
4
∗
0.1
)
+
(
5
∗
0.2
)
+
(
6
∗
0.3
)
+
(
7
∗
0.3
)
=
0.3
+
0.4
+
1
+
1.8
+
2.1
=
5.6
E(X)=(3∗0.1)+(4∗0.1)+(5∗0.2)+(6∗0.3)+(7∗0.3)=0.3+0.4+1+1.8+2.1=5.6

Calculate E(X^2):

𝐸
(
𝑋
2
)
=
(
3
2
∗
0.1
)
+
(
4
2
∗
0.1
)
+
(
5
2
∗
0.2
)
+
(
6
2
∗
0.3
)
+
(
7
2
∗
0.3
)
=
0.9
+
1.6
+
5
+
10.8
+
14.7
=
33
E(X2)=(32∗0.1)+(42∗0.1)+(52∗0.2)+(62∗0.3)+(72∗0.3)=0.9+1.6+5+10.8+14.7=33

Substitute E(X) and E(X^2) into the variance formula to find Var(X):

Answer 1

[AI-generated answer — Bot GPT 3.5]

Var(X) = E(X^2) - (E(X))^2

Var(X) = 33 - (5.6)^2
Var(X) = 33 - 31.36
Var(X) = 1.64

Therefore, the variance of the given data is 1.64.