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Math Help - 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: f_ix_i,\ g_iy_i,\ h_iz_1

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

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

    T can be many different operations.

    for example:

    T may be: ax_i+b

    T may be: ax_i+by_i

    T may be: e^{x_i}

    T may be: lnx_i

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

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

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

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

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

    T may be: [????I don't know how it looks like.], a b c elements drawn from f_ix_i,\ g_iy_i,\ h_iz_1 respectively without replacement. [????I can't figure out the combination]
    Last edited by BookEnquiry; November 28th 2011 at 06:31 AM.
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