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Option 3 : P. R
Explanation:
Let E(x) represent mean
Then by the property of mean
E(Cx) = cE(x) where c is constant
And E(x + c) = E(x) + E(c) = E(x) + c
∴ Options P and R always holds true.
Now,
Let Var (x) represent the variance
Then var (x + c) = var (x) + var (c)
var (x + c) = var (x) {∵ var (c) = 0}
∴ S.D (x + c) = S.D (x)
Now,
var (cx) =(c2)var (x)
S.D (cx) = (c)S.D (x)
∴ Options Q and S are incorrect.
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