Given the sum of (x_i - alpha), the sum of (x_i - beta)^2 and the standard deviation: find alpha and beta
The same question, asked 2 times: 2021 Paper 26*, 1 Feb 2024. Every wording below, oldest first.
Try each one first, then open its answer.
Question 1
2021 Paper 26
83
Let X1,X2,………..X18 be eighteen observation such that ∑i=118(Xi−α)=36 and ∑i=118(Xi−β)2=90, where α and β are distinct real numbers. If the standard deviation of these observations is 1 , then the value of ∣α−β∣ is
Question 2
1 Feb 2024
168
Consider 10 observation x1,x2,…,x10 such that ∑i=110(xi−α)=2 and ∑i=110(xi−β)2=40, where α,β are positive integers. Let the mean and the variance of the observations be 56 and 2584 respectively. Then αβ is equal to:
