Kindly solve them for me, please.
Let Xo be a random sample of size 16 from a normal population with mean and variance, and let X = 02. Let Xz be another independent observation from the same population. State, with reasons, the distribution of:
w - Ex;
U - Z(x - X);
v - Zu - X9'+X;
Let X, Xz, Xo, X1z, W, and U be as defined in the question. State, with reasons, the distribution of:
1s(4X' + X);
Suppose that independent samples (of sizes n) are taken from each of the populations, and that each population is normally distributed with mean and variance σ^2. That is, all populations are normally distributed with the same variance but with (possibly) different means. Let X1, X2, ..., Xk be the respective sample means and variances. Let θ = c1X1 + c2X2 + ... + ckXk, where c1, c2, ..., ck are known constants. Obtain the distribution of θ, providing reasons for any claims you make.
Find the distribution of SSE, where SSE -> χ^2. Provide reasons for any claims you make.