Let (y₁, y₂, ..., yₙ) be independent, normal random variables, each with mean and variance denoted as known constants. Find the density function of the linear combination (u=)

a) (dy₁ + dy₂ + ... + dyₙ)
b) (d(y₁ + y₂ + ... + yₙ))
c) (n ⋅ d(yᵢ))
d) (n ⋅ d(yᵢ²))