MHT CET20242 May 2024Evening ShiftMathematicsStatisticsActual
Consider three observations a, b and c such that b=a+c . If the standard deviation of a +2, ~b +2, c +2 is d, then what holds true.
Options
- Ab^2=3 (a^2+c^2+d^2 )
- Bb ^2= a ^2+ c ^2+3 ~d ^2
- Cb^2=3 (a^2+c^2 )-9 d^2
- Db ^2=3 ( a ^2+ c ^2 )+9 ~d ^2
Correct answer
C. b^2=3 (a^2+c^2 )-9 d^2
Step-by-step solution
Mean of a, b, c is aligned & x = a+b+c 3 & x = 2 b 3 aligned [ b=a+c] S.D. of a+2, b+2, c+2=S . D. of a, b, c aligned d & = a^2+b^2+c^2 3 - ( 2 b 3 )^2 & d^2= a^2+b^2+c^2 3 - 4 b^2 9 & d^2= 3 (a^2+b^2+c^2 )-4 b^2 9 & 9 d^2=3 (a^2+c^2 )-b^2 & b^2=3 (a^2+c^2 )-9 d^2 aligned