(1)二项分布概率公式P{X=k}=C(n,k)p^k(1-p)^(n-k),这题n=4,p=0.5
P{X=0}=C(4,0)0.5^0*0.5^(4-0)=0.5^4;P{X=1}=C(4,1)0.5^1*0.5^(4-1)=4*0.5^4;P{X=2}=C(4,2)0.5^2*0.5^(4-2)=6*0.5^4;P{X=3}=C(4,3)0.5^3*0.5^(4-3)=4*0.5^4;P{X=4}=C(4,4)0.5^4*0.5^(4-4)=0.5^4
概率分布图应该是横坐标是0,1,2,3,4;纵坐标是概率,一共5个点
(2)P{X<2}=P{X=0}+P{X=1}=0.5^4+4*0.5^4=5*0.5^4
(3)P{X≤2}=P{X=0}+P{X=1}+P{X=2}=0.5^4+4*0.5^4+6*0.5^4=11*0.5^4
(4)P{X=0}+P{X=1}+P{X=2}+P{X=3}+P{X=4}=16*0.5^4=1(实际上任何一个二项分布X=0到n的概率全部加起来都是1)
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