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# 有關機率及迴歸的統計應用題目......

Suppose x is a random variable best described by a uniform probability distribution with c=20 and d=45.

(1)Find f(x).

(2)Find the mean and standard deviation of x.

(3)Graph f(x) and locate μ and the interval μ ± 2σ on the graph.

### 2 個解答

• 1 0 年前
最佳解答

(1)Find f(x).

f(X)=1/(45-20) 20 < X < 45

X~U(20,45)

(2)Find the mean and standard deviation of x.

mean=(45+20)/2=32.5 #

Var=((45-20)^2)/12=52.08333333

standard deviation of x

=52.08333333^0.5

=7.216878365 #

(3)Graph f(x) and locate μ and the interval μ 2σ on the graph.

這個自己畫囉，縱軸f(X)橫軸(X)

X介於20~45之間，f(X)的高度1/(45-20)

• f(x)=1/(b-a) for a<= x <=b

E(x)=(a+b)/2

Var(x)=(b-a)^2/12