> coin<-c("H","T")
> coin
[1] "H" "T"
> omega26<-expand.grid(c1=coin,c2=coin,
+ c3=coin,c4=coin)
> omega26
c1 c2 c3 c4
1 H H H H
2 T H H H
3 H T H H
4 T T H H
5 H H T H
6 T H T H
7 H T T H
8 T T T H
9 H H H T
10 T H H T
11 H T H T
12 T T H T
13 H H T T
14 T H T T
15 H T T T
16 T T T T
#카운팅함수 만들기.
> countH<-function(x) sum(x=="H")
> countT<-function(x) sum(x=="T")
> omega26$H_sum<-apply(omega26,1,countH)
> omega26$T_sum<-apply(omega26,1,countT)
> omega26 %>% head()
c1 c2 c3 c4 H_sum T_sum
1 H H H H 4 0
2 T H H H 3 1
3 H T H H 3 1
4 T T H H 2 2
5 H H T H 3 1
6 T H T H 2 2
> #X:동전 4개 동시에 던졌을 때, 나오는 앞면의 수.
> X_prime<-omega26 %>% filter(omega26$H_sum %in% c(0,1))
> X_prime
c1 c2 c3 c4 H_sum T_sum
1 T T T H 1 3
2 T T H T 1 3
3 T H T T 1 3
4 H T T T 1 3
5 T T T T 0 4
> nY2<-omega26 %>% filter(omega26$H_sum >=2) %>% nrow()
> #Y:이산확률변수. E(Y)?
> #E(Y)=X*P(Y=X)+2*P(Y=2)
> PY2<-nY2/nrow(omega26)
> PY2
[1] 0.6875
> nX_prime0<-X_prime %>% filter(X_prime$H_sum ==0) %>% nrow()
> PX_prime0<-nX_prime0/nrow(omega26)
> PX_prime0
[1] 0.0625
> nX_prime1<-X_prime %>% filter(X_prime$H_sum ==1) %>% nrow()
> PX_prime1<-nX_prime1/nrow(omega26)
> PX_prime1
[1] 0.25
> 0*PX_prime0+1*PX_prime1+2*PY2
[1] 1.625
> 0*PX_prime0+1*PX_prime1+2*PY2==13/8
[1] TRUE
