A family with a mother, father, two daughters and three sons lines up in a random...

A family with a mother, father, two daughters and three sons lines up in a random order for a photo.
1. (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?
2. (b) What are the expectations E[D1] and E[D2]?
3. (c) Use linearity of expectation to compute E[D].
4. (d) Let N be the random variable denoting the number of sons who are standing next to the mother. Use appropriate indicator variables together with linearity of expec- tation to find E[N]. State where you are using linearity of expectation.

Expert Solution

orchestra answered 2 years ago

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