To find the distribution list of x, we need to find the probabilities of X=0, X= 1, X=2, X=3 and X=4 respectively:
P(X=4)=0, this is because four out of five people in this age group have recited it-there is no possibility that "two people randomly selected from these five people have not recited it"! ! !
Therefore, it can be said that there are only four possibilities for the value of the random variable X: 0, 1, 2, 3.
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P(X=0)=P (4 people randomly selected for memory)
=P (2 people are randomly selected according to their age groups and all of them are memorized &; Randomly select 2 people's memories by age group)
=P (two people randomly selected from age group memory) *P (two people randomly selected from age group memory)
=C(4，2)/C(5，2)*C(3，2)/C(5，2)
=0.6*0.3=0. 18
Similarly,
P(X= 1)=P (3 of 4 randomly selected people in memory)
=P (2 people are randomly selected according to their age groups and all of them are memorized &; 65438+ 0) of 2 people randomly selected by age+
P (1 randomly select two people's memories by age group &; Randomly select 2 people's memories by age group)
=P (2 people were randomly selected according to the remembered age group) *P (65438+ 0 people were randomly selected according to the remembered age group)+
P (1 2 randomly selected by the remembered age group) *P (2 randomly selected by the remembered age group)
=C(4，2)/C(5，2)*C(3， 1)*C(2， 1)/C(5，2)+C(4， 1)*C( 1， 1)/C(5，2)*C(3，2)/C(5，2)
=0.6*0.6+0.4*0.3=0.48
Besides,
P(X=2)=P (2 of 4 randomly selected people in memory)
=P (2 people are randomly selected according to their age groups and all of them are memorized &; 0 of 2 people randomly selected by age)+
P (1 randomly select two people's memories by age group &; 65438+ 0) of 2 people randomly selected by age+
P (0 memory of 2 people is randomly selected according to age group &; Randomly select 2 people's memories by age group)
=C(4，2)/C(5，2)*C(2，2)/C(5，2)+C(4， 1)*C( 1， 1)/C(5，2)*C(3， 1)*C(2， 1)/C(5，2)+0
=0.6*0. 1+0.4*0.6=0.3
Besides,
P(X=3)=P (65438+ 0 of 4 randomly selected people)
=P (1 randomly select two people's memories according to their age groups &; 0 of 2 people randomly selected by age group)
=C(4， 1)/C(5，2)*C(2，2)/C(5，2)
=0.4*0. 1=0.04
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Mathematical expectation = (sum of distribution lists of x) x*P(X=x)
= 1*0.48+2*0.3+3*0.04
= 1.2