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
5√6
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B
√56
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C
30
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D
√30
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Solution
The correct option is B√56 If the S.D. of variate X is . σ(X)=√∑Ni=1(Xi−¯¯¯¯X)2N σ(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