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Thread: How to find the mean and variance of new combinations of old population?

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    How to find the mean and variance of new combinations of old population?

    I'm a late learner of maths &science.
    Any books discuss these kind of problems?

    3 groups of data: $\displaystyle f_ix_i,\ g_iy_i,\ h_iz_1$

    f g h are their frequencies.
    mean: $\displaystyle \bar{x},\ \bar{y},\ \bar{z}$
    variance: $\displaystyle \sigma_x,\ \sigma_y,\ \sigma_z$

    Find the mean and variance of $\displaystyle T(f_ix_i,\ g_iy_i,\ h_iz_i)$

    T can be many different operations.

    for example:

    T may be: $\displaystyle ax_i+b$

    T may be: $\displaystyle ax_i+by_i$

    T may be: $\displaystyle e^{x_i}$

    T may be: $\displaystyle lnx_i$

    T may be: $\displaystyle x_i+x_j$, mean of two elements drawn from $\displaystyle f_ix_i$ with replacement i=j is allowed. $\displaystyle n^2$

    T may be: $\displaystyle x_i+x_j$, two elements drawn from $\displaystyle f_ix_i$ without replacement where $\displaystyle i\ \neq\ j$. $\displaystyle C^n_2$

    T may be: [????I don't know how it looks like.] is $\displaystyle P^n_2$

    T may be: $\displaystyle x_i+x_j+x_k$, three elements drawn from $\displaystyle f_ix_i$ without replacement where $\displaystyle i\ \neq\ j\ \neq\ k$. $\displaystyle C^n_3{$

    T may be: $\displaystyle ax_i+by_i+cz_i$, a b c elements drawn from $\displaystyle f_ix_i,\ g_iy_i,\ h_iz_1$ respectively with replacement. $\displaystyle n^{a+b+c}$

    T may be: [????I don't know how it looks like.], a b c elements drawn from $\displaystyle f_ix_i,\ g_iy_i,\ h_iz_1$ respectively without replacement. $\displaystyle [????$I can't figure out the combination]
    Last edited by BookEnquiry; Nov 28th 2011 at 05:31 AM.
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