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Given that `barx` is the mean and `sigma^2` is the variance of n observations `x_1,x_2`,….,`x_n`. Prove that the mean and variance of the observations `ax_1,ax_2`, .., `ax_n`, are `abarx` and `a^2sigma^2` respectively `(a ne 0)`.

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Knowledge Check

  • If the mean of a set of observations x_(1),x_(2), …,x_(n)" is " bar(X) , then the mean of the observations x_(i) +2i , i=1, 2, ..., n is

    A
    `bar(X) +2`
    B
    `bar(X) +2n`
    C
    `bar(X)+(n+1)`
    D
    `X+n`

  • If mean and standard deviation of 5 observations x_1,x_2,x_3,x_4 are 10 and 3 respectively , then the variance of 6 observation x_1,x_2,…..x_5 and -50 is equal to:

    A
    `582.5`
    B
    ` 507.5`
    C
    ` 586.5`
    D
    ` 509.5`

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    A
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    B
    `alphasigma^(2)`
    C
    `alpha^(2)sigma^(2)`
    D
    `(sigma^(2))/(alpha^(2))`

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