Answer:
Mean = 35
Variance = 291.7
Step-by-step explanation:
Data provided in the question:
X : 1, 2, 3, 4, 5, 6
All the data are independent
Thus,
The mean for this case will be given as:
Mean, E[X] = [tex]\frac{\textup{Sum of all the observations}}{\textup{Total number of observations}}[/tex]
or
E[X] = [tex]\frac{\textup{1+2+3+4+5+6}}{\textup{6}}[/tex]
or
E[X] = 3.5
For 10 days, Mean = 3.5 × 10 = 35
And,
variance = E[X²] - ( E[X] )²
Now, for this case of independent value,
E[X²] = [tex]\frac{1^2+2^2+3^2+4^2+5^2+6^2}{\textup{6}}[/tex]
or
E[X²] = [tex]\frac{1+4+9+16+25+36}{\textup{6}}[/tex]
or
E[X²] = [tex]\frac{91}{\textup{6}}[/tex]
or
E[X²] = 15.167
Therefore,
variance = E[X²] - ( E[X] )²
or
variance = 15.167 - 3.5²
or
Variance = 2.917
For 10 days = Variance × Days²
= 2.917 × 10²
= 291.7
