Rules for means and variances If X is a random variable and a and b are fixed numbers, then µ a+bX = a + bµ X σ 2 a+bX = b 2 σ 2 X If X and Y are two independent random variables, then µ X+Y = µ X + µ Y σ 2 X+Y = σ 2 X + σ 2 Y If X and Y are NOT independent but have correlation ρ, then µ X+Y = µ X + µ Y σ 2 X+Y = σ 2 X + σ 2 Y + 2ρσ X σ Y
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