====== 이산형 균일분포 (Discrete Uniform Distribution) ======
===== 정의 =====
===== 표기 =====
 $R_{x} \in \{ \ 1 \ , \ 2 \ , \cdots , \ N \ \} $이라고 정의 할 때
===== 받침 =====
 $$ x \in \{ \ 1 \ , \ 2 \ , \cdots , \ N \ \} $$
===== 확률질량함수 =====
 $$ p(x) = \frac{1}{N} $$

<plot>
 set title "Discrete Uniform Distribution PMF"
 set size 1.0
 set xtics (1,2,3,4,5,6)
 set xrange [0.5:6.5]
 set yrange [0:0.5]
 set format x "%.1f"
 set format y "%.2f"
 set xlabel "x"
 set ylabel "p(x)"

 plot 1/6.0 title "N=6"
</plot>
===== 누적분포함수 =====
 $$ F(x) = \frac{x}{N} $$

<plot>
 set title "Discrete Uniform Distribution CDF"
 set size 1.0
 set xtics (1,2,3,4,5,6)
 set xrange [0.5:6.5]
 set yrange [0:1.1]
 set format x "%.1f"
 set format y "%.2f"
 set xlabel "x"
 set ylabel "F(x)"
 set key left

 f(x,n) = int(x)/n

 plot f(x+0.5,6.0) with steps title "N=6"
</plot>
===== 기대값 =====
 $$ E(X) = \frac{N+1}{2} $$
===== 분산 =====
 $$ Var(X) = \frac{N^{2}-1}{12} $$

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  * [[분포]]