7.15 Assume that X₁, X2, X3, X4 are independent and normally distributed with E[X₁] = 100 E[X₂] = 90 E[X3] = 95 E[X4] = 105 Var[X₁] = 30 Var[X₂] = 20 Var[X3] = 25 Var[X4] = 15. (a) What is the distribution of S = X₁ +X-2 + X3 + X4? Can we use the central limit theorem in this case? (b) Find E[S], Var[S], and o [S]. (e) Compute P(S≤ 390). Is the answer different from P(S < 390)?

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