a. If N ~ N(1, 4), how is M = 3N + 5 distributed?

b. If L ~ (1, 3), how is G = log(L) distributed?

c. If N ~ N(2, 6), how is E = e^N distributed?

d. If N₁ ~ N(0, 9) and N₂ ~ N(2, 1) have correlation 0.3, how is M = N₁ + 3N₂ distributed?

e. If N₁ ~ N(1, 1) and N₂ ~ N(0, 4) are independent, how is M = 2N₁ + N₂ distributed?

f. If N ~ N(0, 1), how is H = N ² distributed?

g. If N₁ ~ N(0, 1) and N₂ ~ N(0, 1) are independent, how is distributed?

h. If X ~ (1, 0), how is C = distributed?

b. By [3.91] and [3.92], L ~ .

c. By [3.87] and [3.88], E ~ (e⁵, e¹⁶ – e¹⁰).

d. We cannot say. We are not told if N₁ and N₂ are joint-normal.

e. Because N₁ and N₂ are independent, they are joint-normal. Hence, M is normal. By [3.27] and [3.28], M ~ N(2, 6).

f. H ~ (1, 0)

g. H ~ (2, 25)

h. This is a nonstandard distribution. It is clearly not normal because C is strictly positive.