Question

**question 01)** Let * X_{i} , i
= 1 , 2 , 3 , … , 10* be normally distributed
independent random variables

and the standard deviation **σ =
.....................** (round to the third decimal place),
if it is known that **1/10 ∑ ^{10}_{i=1}
X_{i} ∼ N ( 1.5 , 0.3 ).**

**need ****μ and**
**σ**

Answer #1

* X i ∼ N ( μ , σ^2 )*.

That is * X i ∼ N ( 1.5 , 0.3 )*.

Mean = 1.5

Standard deviation = answer.

Example to calculate mean and standard deviation from 10 random variables:

Sample : {1,2,3,4,5,6,7,8,9,10}

Mean = sum of Xi / total variables

Mean = 5.5

(formula used for sum : sum of 1st n natural number that 1+2+3.....+n = n(n+1)/2}

Standard deviation :

x(i) | x(i) - mean | (x(i)-mean)^2 | ||

1 | -4.5 | 20.25 | ||

2 | -3.5 | 12.25 | ||

3 | -2.5 | 6.25 | ||

4 | -1.5 | 2.25 | ||

5 | -0.5 | 0.25 | ||

6 | 0.5 | 0.25 | ||

7 | 1.5 | 2.25 | ||

8 | 2.5 | 6.25 | ||

9 | 3.5 | 12.25 | ||

10 | 4.5 | 20.25 | ||

Sum = | 82.5 |

Standard deviation :

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Definition
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