1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Let X be a variate taking values x1,x2,.....xn and Y be a variate taking values y1,y2,.....yn such that yi=6xi+3;i=1,2,....n. If Var(Y)=30, then σX is equal to

A
56
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
56
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B √56If the S.D. of variate X is . σ(X)=√∑Ni=1(Xi−¯¯¯¯X)2Nσ(aX+b)=√∑Ni=1(xi−¯¯¯x)2N = √[(aX1+b)−(a¯¯¯¯X+b)]2+[(aX2+b)−(a¯¯¯¯X+b)]2+....+[(aXN+b)−(a¯¯¯¯X+b)]2N = √a2[(X1−¯¯¯¯X)2+(X2−¯¯¯¯X)2+...+(XN−¯¯¯¯X)2]N = |a|√∑Ni=1(Xi−¯¯¯¯X)2N = |a|σ(X) Given Var(Y)=30=>(σ(Y))2=30=>σ(Y)=√30=>σ(6X+3)=√30 σ(Y)=σ(aX+b)=|a|σ(X)=>σ(6X+3)=6×σ(X)=>√30=6×σ(X)=>σ(X)=√306=>σ(X)=√56

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Definition of Function
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program