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Which of the following is the standard deviation of the random variable x

Which of the following is the standard deviation of the random variable x-example-1
User Soshika
by
8.2k points

1 Answer

5 votes

Answer: B. 1.414

Explanation:

let x be the random variable denotes the number of die.

Numbers on 5-faced die = 1,2,3,4,5

Probability of getting any number =
(1)/(5)

Mean =
\bar {x}=\sum p_ix_i


\\\\\Rightarrow\bar{x}=(1)/(5)(1)+(1)/(5)(2)+(1)/(5)(3)+(1)/(5)(4)+(1)/(5)(5)\\\\=(1)/(5)(1+2+3+4+5)\\\\=(1)/(5)(15)=3

Standard deviation:
\sigma=\sum \sqrt{\frac{(x_i-\bar{x})^2}{N}}


=\sqrt{((1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2)/(5)}\\\\=\sqrt{(4+1+0+1+4)/(5)}\\\\=\sqrt{(10)/(5)}\\\\=√(2)\approx1.414

Hence, the standard deviation of the random variable x is 1.414.

Thus, the correct option is B.

User Trinimon
by
7.7k points

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