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# s1 hard discrete random variable question= how do you answer this? Solomon paper q5

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1. The letters of the word DISTRIBUTION are written on separate cards. The cards are then shuffled and the top three are turned over.
Let the random variable V be the number of vowels that are turned over.
(a) Show that P(V = 1) = 21/44 . (3 marks)
(b) Find the probability distribution of V. (4 marks)
(c) Find E(V) and Var(V). (6 marks)
2. (Original post by N123456789)
The letters of the word DISTRIBUTION are written on separate cards. The cards are then shuffled and the top three are turned over.
Let the random variable V be the number of vowels that are turned over.
(a) Show that P(V = 1) = 21/44 . (3 marks)
(b) Find the probability distribution of V. (4 marks)
(c) Find E(V) and Var(V). (6 marks)
Seems more like an S2 question than S1 but it is too late in the day for me.
3. (Original post by N123456789)
The letters of the word DISTRIBUTION are written on separate cards. The cards are then shuffled and the top three are turned over.
Let the random variable V be the number of vowels that are turned over.
(a) Show that P(V = 1) = 21/44 . (3 marks)
(b) Find the probability distribution of V. (4 marks)
(c) Find E(V) and Var(V). (6 marks)
a) Draw a tree diagram and see what could happen
b) Draw a graph with 0 to 3 on the x axis and the 0 to 1 on the y-axis. Now make a bar representing the probability of 0, 1, 2, and 3 vowels based on your tree diagram.
c) Use the formula, we are discrete so sum of P(X=x)*x for 0 to 3 based on the graph.
4. (Original post by brainhuman)
a) Draw a tree diagram and see what could happen
b) Draw a graph with 0 to 3 on the x axis and the 0 to 1 on the y-axis. Now make a bar representing the probability of 0, 1, 2, and 3 vowels based on your tree diagram.
c) Use the formula, we are discrete so sum of P(X=x)*x for 0 to 3 based on the graph.

the mark scheme shows the probabilities falling on each branch of the tree diagram therefore, picking up the 3 cards means that they are not replaced. Why are the cards not replaced? I don't understand that aspect..

it doesn't actually say in the question whether the cards picked are replaced....
5. (Original post by N123456789)
the mark scheme shows the probabilities falling on each branch of the tree diagram therefore, picking up the 3 cards means that they are not replaced. Why are the cards not replaced? I don't understand that aspect..

it doesn't actually say in the question whether the cards picked are replaced....
If it doesn't say that things are replaced, then you can assume they aren't replaced.
6. (Original post by N123456789)
the mark scheme shows the probabilities falling on each branch of the tree diagram therefore, picking up the 3 cards means that they are not replaced. Why are the cards not replaced? I don't understand that aspect..

it doesn't actually say in the question whether the cards picked are replaced....
i think once they`re turned over it`s implied that they`re out of consideration i.e not replaced
7. (Original post by Zacken)
If it doesn't say that things are replaced, then you can assume they aren't replaced.
is that with all s1 probability questions ?
8. (Original post by N123456789)
is that with all s1 probability questions ?
Yep.
9. (Original post by N123456789)
the mark scheme shows the probabilities falling on each branch of the tree diagram therefore, picking up the 3 cards means that they are not replaced. Why are the cards not replaced? I don't understand that aspect..

it doesn't actually say in the question whether the cards picked are replaced....
"The cards are then shuffled and the top three are turned over."

There is no replacement.
10. Thank you all

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