1.
令P: probability measure
令X為選購3台電腦的瑕疵數
P(X = 0) = C(20, 3)/C(25, 3) = 57/115
P(X = 1) = C(20, 2)C(5, 1)/C(25, 3) = 19/46
P(X = 2) = C(20, 1)C(5, 2)/C(25, 3) = 2/23
P(X = 3) = C(5, 3)/C(25, 3) = 1/230
2. (a)
for all x in (-1, 3), f(x)=3x2/28 ≧ 0
for all x in R - (-1, 3), f(x) = 0 ≧ 0
=> for all x in R f(x) ≧ 0
∫(-∞, ∞ ) f(x) dx = ∫(-1, 3 ) 3x2/28 dx = x3/28 |(-1, 3) = 1
so f(x): probability density function
2. (b)
P(0 < X ≤ 0) = ∫(0, 1 ) 3x2/28 dx = 1/28
2. (c)
不懂和(b)的差異.
3.
E[x] = ∫(-∞, ∞ ) xf(x) dx = ∫(-1, 3 ) 3x3/28 dx = 15/7
E[g(X)] = E[5X + 6] = 5E[X] + 6 = 117/7
我機率不行, 只會這些, 有誤請糾正.