Mean:
E[Y] = E[3X₁ + X₂]
E[Y] = 3 E[X₁] + E[X₂]
E[Y] = 3µ + µ
E[Y] = 4µ
Variance:
Var[Y] = Var[3X₁ + X₂]
Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]
(the covariance is 0 since X₁ and X₂ are independent)
Var[Y] = 9 Var[X₁] + Var[X₂]
Var[Y] = 9σ² + σ²
Var[Y] = 10σ²
