Question

Find the mean and variance of the number randomly selected from 1 to 15.​

Answer 1

square each value and multiply by its probability. sum them up and we get Σx2p. then subtract the square of the Expected Value μ.

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Answer 2

Answer:

Mean and variance of the number randomly selected from 1 to 15 is 8 and $\frac{56}{3}$ respectively.

Step-by-step explanation:

The mean of a number randomly selected from 1 to 15 are:

$m(x) = \frac{1}{n} (x_{1} +x_{2}+x_{3}+...+x_{15})=\frac{1}{15}(1+2+3+...+15)=8$

The variance of a number randomly selected from 1 to 15 are:

$V= \frac{1}{N}(summation of 1 to15 (x_{i}-m)) ^{2} =\frac{1}{15}(49+36+25+16+9+4+1+0+1+4+9+16+25+36+49)\\ =\frac{2}{15}(49+36+25+16+9+4+1)\\\\=\frac{2}{15}*\frac{7*8*15}{6} =\frac{56}{3}$

Hence, Mean and variance of the number randomly selected from 1 to 15 is 8 and $\frac{56}{3}$ respectively.