The following results on summations will help us in calculating the sample variance s?. For any constant c, the following apply. 1. C = nc i = 1 Cy i = C 2. i = i = 1 3. (x; + Y;) Yi i = 1 i = 1 Use 1, 2, and 3 to show that 2 1 s2 = (Y, - 7)² = n - 1 i = 1 n - 1

The mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. You are now being told they are independent. Find the value of each requested parameter A. The mean of T= -3x +20 is ___ B. The mean of W= Y - X is ___ C. The variance of D = X - 2Y is ___

Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. Does tach increase, decrease, or stay the same? (M-u) (M-u)Vn The size of the Z-score Z. = M-u – OM (M-u) The size of Cohen's d d = (Mcr-u) (Mcr-u)vn The power P( 2Z> Mcritical-µu

Let X₁, X2,..., be a sequence of independent and identically distributed random variables, each with a mean value x and variance ok, both of which are assumed to be finite. Let N be a discrete random variable independent of X₁, X2,..., and assuming values in the set {0, 1, 2, ...}, with mean value N and variance ok (both are finite). Form the random-compound sum Y=1 Xk, with the convention Y = 0 whenever N = 0.