Y(xˉ)=axˉ+b=17a(1+2+3+….+17)+b=1717×2a(17×18)+b=17
9a+b=17
σ(X2)=n∑x2−(n∑x)2
=1712+22+…+172−(171+2+...+17)2
=6⋅1717⋅18⋅35−(2⋅1717⋅18)2
=105−81=24
∴σ(Y2)=a2σ(X2)=a2⋅24=216
⇒a2=24216=9
a=3
∴b=17−27
∴b=17−27
b=−10
∴a+b=−7
Let X=x∈N:1≤x≤17 and Y=ax+b:x∈Xanda,b∈R,a>0. If mean and variance of elements of Y are 17 and 216 respectively then a+b is equal to
Held on 2 Sept 2020 · Verified 6 Jul 2026.
7
−7
−27
9
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