Probability and permutations relationship












0














A family with a mother, father, two daughters
and three sons lines up in a random order for a photo.
(a) Let D be the random variable denoting the number of daughters who are standing next to the mother and for i = 1,2 let Di be the indicator variable that is 1 if daughter i is next to the mother and 0 otherwise. What is the relationship between D, D1, and D2?
Solution: D = D1 + D2



Well, I don't really get the logic here...










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  • What part don't you get? Do you know the definition of an indicator variable?
    – lulu
    Dec 28 '18 at 20:15
















0














A family with a mother, father, two daughters
and three sons lines up in a random order for a photo.
(a) Let D be the random variable denoting the number of daughters who are standing next to the mother and for i = 1,2 let Di be the indicator variable that is 1 if daughter i is next to the mother and 0 otherwise. What is the relationship between D, D1, and D2?
Solution: D = D1 + D2



Well, I don't really get the logic here...










share|cite|improve this question






















  • What part don't you get? Do you know the definition of an indicator variable?
    – lulu
    Dec 28 '18 at 20:15














0












0








0







A family with a mother, father, two daughters
and three sons lines up in a random order for a photo.
(a) Let D be the random variable denoting the number of daughters who are standing next to the mother and for i = 1,2 let Di be the indicator variable that is 1 if daughter i is next to the mother and 0 otherwise. What is the relationship between D, D1, and D2?
Solution: D = D1 + D2



Well, I don't really get the logic here...










share|cite|improve this question













A family with a mother, father, two daughters
and three sons lines up in a random order for a photo.
(a) Let D be the random variable denoting the number of daughters who are standing next to the mother and for i = 1,2 let Di be the indicator variable that is 1 if daughter i is next to the mother and 0 otherwise. What is the relationship between D, D1, and D2?
Solution: D = D1 + D2



Well, I don't really get the logic here...







discrete-mathematics






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share|cite|improve this question










asked Dec 28 '18 at 20:02









Tom1999Tom1999

445




445












  • What part don't you get? Do you know the definition of an indicator variable?
    – lulu
    Dec 28 '18 at 20:15


















  • What part don't you get? Do you know the definition of an indicator variable?
    – lulu
    Dec 28 '18 at 20:15
















What part don't you get? Do you know the definition of an indicator variable?
– lulu
Dec 28 '18 at 20:15




What part don't you get? Do you know the definition of an indicator variable?
– lulu
Dec 28 '18 at 20:15










1 Answer
1






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oldest

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0














The possible positions of the mother and two daughters are as follows: (where $x$ represents a person other than the daughters)
begin{align*}
ldots,x,m,d_i, x,x,ldots\
ldots,d_i,m,x,x,ldots\
ldots,d_i,m,d_j, x,x,ldots\
ldots,x,m,x,x,ldots\
end{align*}

In the first two cases, $D=1$, in the third case $D=2$, and in the last case $D=0$.



Likewise, in the first two cases, one of the indicator functions takes on the value $1$ and the other $0$. So $D=D_1+D_2$.



You can deal with the remaining cases similarly.






share|cite|improve this answer























  • Thank you Anurag :)
    – Tom1999
    Dec 28 '18 at 21:43











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1 Answer
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active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














The possible positions of the mother and two daughters are as follows: (where $x$ represents a person other than the daughters)
begin{align*}
ldots,x,m,d_i, x,x,ldots\
ldots,d_i,m,x,x,ldots\
ldots,d_i,m,d_j, x,x,ldots\
ldots,x,m,x,x,ldots\
end{align*}

In the first two cases, $D=1$, in the third case $D=2$, and in the last case $D=0$.



Likewise, in the first two cases, one of the indicator functions takes on the value $1$ and the other $0$. So $D=D_1+D_2$.



You can deal with the remaining cases similarly.






share|cite|improve this answer























  • Thank you Anurag :)
    – Tom1999
    Dec 28 '18 at 21:43
















0














The possible positions of the mother and two daughters are as follows: (where $x$ represents a person other than the daughters)
begin{align*}
ldots,x,m,d_i, x,x,ldots\
ldots,d_i,m,x,x,ldots\
ldots,d_i,m,d_j, x,x,ldots\
ldots,x,m,x,x,ldots\
end{align*}

In the first two cases, $D=1$, in the third case $D=2$, and in the last case $D=0$.



Likewise, in the first two cases, one of the indicator functions takes on the value $1$ and the other $0$. So $D=D_1+D_2$.



You can deal with the remaining cases similarly.






share|cite|improve this answer























  • Thank you Anurag :)
    – Tom1999
    Dec 28 '18 at 21:43














0












0








0






The possible positions of the mother and two daughters are as follows: (where $x$ represents a person other than the daughters)
begin{align*}
ldots,x,m,d_i, x,x,ldots\
ldots,d_i,m,x,x,ldots\
ldots,d_i,m,d_j, x,x,ldots\
ldots,x,m,x,x,ldots\
end{align*}

In the first two cases, $D=1$, in the third case $D=2$, and in the last case $D=0$.



Likewise, in the first two cases, one of the indicator functions takes on the value $1$ and the other $0$. So $D=D_1+D_2$.



You can deal with the remaining cases similarly.






share|cite|improve this answer














The possible positions of the mother and two daughters are as follows: (where $x$ represents a person other than the daughters)
begin{align*}
ldots,x,m,d_i, x,x,ldots\
ldots,d_i,m,x,x,ldots\
ldots,d_i,m,d_j, x,x,ldots\
ldots,x,m,x,x,ldots\
end{align*}

In the first two cases, $D=1$, in the third case $D=2$, and in the last case $D=0$.



Likewise, in the first two cases, one of the indicator functions takes on the value $1$ and the other $0$. So $D=D_1+D_2$.



You can deal with the remaining cases similarly.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 28 '18 at 20:45

























answered Dec 28 '18 at 20:20









Anurag AAnurag A

25.8k12249




25.8k12249












  • Thank you Anurag :)
    – Tom1999
    Dec 28 '18 at 21:43


















  • Thank you Anurag :)
    – Tom1999
    Dec 28 '18 at 21:43
















Thank you Anurag :)
– Tom1999
Dec 28 '18 at 21:43




Thank you Anurag :)
– Tom1999
Dec 28 '18 at 21:43


















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