Discrete random variables and their distribution Understand discrete random variables, their distribution and numerical characteristics, the binomial distribution, and the hypergeometric distribution.
Practice questions 1 从1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 X X X X X X E ( X ) = ( ) E(X)=(\quad) E ( X ) = ( ) 3 2 \dfrac{3}{2} 2 3 2 在东京奥运会中，甲、乙、丙三名跳水运动员参加小组赛，已知甲晋级的概率为p ( 0 < p < 1 ) p(0< p< 1) p ( 0 < p < 1 ) q ( 0 < q < 1 ) q(0< q< 1) q ( 0 < q < 1 ) 3 设随机变量X ～ B ( 2 , p ) X～B(2,p) X ～ B ( 2 , p ) Y ～ B ( 3 , p ) Y～B(3,p) Y ～ B ( 3 , p ) P ( X ⩾ 1 ) = 5 9 P(X\geqslant 1)=\dfrac{5}{9} P ( X ⩾ 1 ) = 9 5 D ( 3 Y + 1 ) = D\left( \sqrt{3}Y+1\right) = D ( 3 Y + 1 ) = 2 2 2 3 3 3 4 一袋中有5 5 5 3 3 3 10 10 10 ξ ξ ξ P ( ξ = 12 ) P(ξ=12) P ( ξ = 12 ) ( ) () ( ) C 12 10 ( 3 8 ) 10 ⋅ ( 5 8 ) 2 C_{12}^{10}( \dfrac {3}{8})^{10}⋅( \dfrac {5}{8})^{2} C 12 10 ( 8 3 ) 10 ⋅ ( 8 5 ) 2 5 设随机变量X X X P ( X = i ) = i 2 a , i = 1 , 2 , 3 P(X=i)= \dfrac{i}{2a},i=1,2,3 P ( X = i ) = 2 a i , i = 1 , 2 , 3 P ( X = 2 ) = ( ) P(X=2)=() P ( X = 2 ) = ( ) 1 3 \dfrac{1}{3} 3 1 1 6 \dfrac{1}{6} 6 1 1 9 \dfrac{1}{9} 9 1