Question

Which of the following is the standard deviation of the random variable x, the number that appears on a die, if the probability of any number on a fair, 9-sided die is 1/9?

A.2.582
B.2.739
C.0.11
D.4.5

Answer 1

i got C as the answer

Answer 2

Answer with explanation:

When a dice with 9 faces are rolled total possible outcome =9

→x={1,2,3,4,5,6,7,8,9}

Probability of getting any number from 1 to 9 , when the die is rolled once

`=(1)/(9)`

`E(x)=1* (1)/(9)+2* (1)/(9)+3* (1)/(9)+4* (1)/(9)+5* (1)/(9)+6* (1)/(9)+7* (1)/(9)+8* (1)/(9)+9* (1)/(9)\\\\E(x)=(1+2+3+4+5+6+7+8+9)* (1)/(9)\\\\E(x)=5`

`E(x^2)=1^2* (1)/(9)+2^2* (1)/(9)+3^2* (1)/(9)+4^2* (1)/(9)+5^2* (1)/(9)+6^2* (1)/(9)+7^2* (1)/(9)+8^2* (1)/(9)+9^2* (1)/(9)\\\\E(x)=(1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2)* (1)/(9)\\\\E(x)=(9 * 10 * 19* 1)/(6 * 9)\\\\E(x)=(95)/(3)`

Standard Deviation

`=√(E(x^2)-(E(x))^2)\\\\=\sqrt{(95)/(3)-5^2}\\\\=\sqrt{(95-75)/(3)}\\\\=\sqrt{(20)/(3)}\\\\=√(6.67)\\\\=2.5819\\\\=2.582`

Option A→2.582