Let X be a Gaussian random variable with mean µ and standard deviation σ. (a) Find the pdf of Y = (2X + 5) in terms of µ and σ. (b) Evaluate E[(2X + 5) 2 ] in terms of µ and σ. (c) If µ = 5, find σ so that P(X > 9) = 0.2. (d) If µ = 12 and σ 2 = 4, find the value of λ so that P(X > λ) = 0.10.