Apply the transformation rules to Y = 250 + 40X with μ = 0.95 and σ² = 0.9475, then the sum rules to five independent batches.

Answer

import math mu, var = 0.95, 0.9475 a, b = 40, 250 ey = a * mu + b vy = a * a * var print(f"E[Y]={ey:.2f} Var(Y)={vy:.2f} SD(Y)={math.sqrt(vy):.2f}") k = 5 print(f"sum of {k}: E={k * mu:.2f} Var={k * var:.4f} SD={math.sqrt(k * var):.2f}")

Authored from first principles — no ADAPT source states these rules; H-W7 uses them for Var(X̄) (shape only); original dataset