A point D is chosen on the line AB, whose midpointis C and whose length is a. If X, the distance from D toA, is a random variable having the uniform density withα = 0 and β = a, what is the probability that AD, BD,and AC will form a triangle?

Under the SLR model, Y₁, Y2, . . ., Y, are independent normal random variables with E[Y;] = ẞo + ẞ₁x; and V(Y;) = σ², for i = 1, 2, ..., n. a. Compute the likelihood function, L(y1, 2, ..., Yn Bo, ß1,0²) = L(ẞ0, B1, 0²). b. Show that the MLE of o² is SSE [the MLEs of n Bo and B₁ are the same as the least-squares estimators, Bo and B₁.]

Suppose we have three independent random variables X, Y and Z where... Var(X + 2Y) = 13, Var(2Y + 4Z) = 40, and Var(Z) = 2. a) If E(Y) = E(Z) = 1, what is E(Y2+Z2)? b) What is SD(X + Y + Z)?

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