Let the observations xi(1≤i≤10) satisfy the equations, 10∑i=1(xi−5)=10 and 10∑i=1(xi−5)2=40. If μ and λ are the mean and the variance of observations, (x1−3),(x2−3),...,(x10−3), then the ordered pair (μ,λ) is equal to :
A
(6,3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(3,6)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(3,3)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(6,6)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C(3,3) 10∑i=1(xi−5)=10 ⇒10∑i=1xi−50=10 ⇒10∑i=1xi=60
μ=10∑i=1(xi−3)10=10∑i=1xi−3010=3
Variance is unchanged, if a constant is added or subtracted from each observation ∴λ=Var(xi−3)=Var(xi−5) =10∑i=1(xi−5)210−⎛⎜
⎜
⎜
⎜⎝10∑i=1(xi−5)10⎞⎟
⎟
⎟
⎟⎠2 =4010−(1010)2 =3