Is there an intuitive explanation for the probability mass function of Y that you discovered?
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Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from
the urn repeatedly with replacement, until I see the first green or yellow ball, and then I stop. Let
N be the number draws I needed. Let Y equal 1 if the last draw is green and 2 if the last draw is
yellow. Find the joint and marginal probability mass functions of N and Y and determine whether
N and Y are independent. Is there an intuitive explanation for the probability mass function of Y
that you discovered?
I'm completely loss and can't even start. From what I understand, $N sim Geom(frac{7}{9})$, but I can't get what is the distribution of Y. What is the pmf of Y? And how to find joint pmf? Thank you.
probability
asked Nov 14 at 5:12
dxdydz
999
add a comment |
up vote
0
down vote
favorite
Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from
the urn repeatedly with replacement, until I see the first green or yellow ball, and then I stop. Let
N be the number draws I needed. Let Y equal 1 if the last draw is green and 2 if the last draw is
yellow. Find the joint and marginal probability mass functions of N and Y and determine whether
N and Y are independent. Is there an intuitive explanation for the probability mass function of Y
that you discovered?
I'm completely loss and can't even start. From what I understand, $N sim Geom(frac{7}{9})$, but I can't get what is the distribution of Y. What is the pmf of Y? And how to find joint pmf? Thank you.
probability
asked Nov 14 at 5:12
dxdydz
999
Events defining $Y$ do not cover whole event space.
– keoxkeox
Nov 14 at 5:25
If the person asking the question is OK with measures not adding up to 1 then $Y sim (4/9) delta(x-1) + (3/9) delta(x-2)$
– keoxkeox
Nov 14 at 5:30
Also your joint pmf will add up to $7/9$
– keoxkeox
Nov 14 at 5:32
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from
the urn repeatedly with replacement, until I see the first green or yellow ball, and then I stop. Let
N be the number draws I needed. Let Y equal 1 if the last draw is green and 2 if the last draw is
yellow. Find the joint and marginal probability mass functions of N and Y and determine whether
N and Y are independent. Is there an intuitive explanation for the probability mass function of Y
that you discovered?
I'm completely loss and can't even start. From what I understand, $N sim Geom(frac{7}{9})$, but I can't get what is the distribution of Y. What is the pmf of Y? And how to find joint pmf? Thank you.
probability
asked Nov 14 at 5:12
dxdydz
999
Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from
the urn repeatedly with replacement, until I see the first green or yellow ball, and then I stop. Let
N be the number draws I needed. Let Y equal 1 if the last draw is green and 2 if the last draw is
yellow. Find the joint and marginal probability mass functions of N and Y and determine whether
N and Y are independent. Is there an intuitive explanation for the probability mass function of Y
that you discovered?
I'm completely loss and can't even start. From what I understand, $N sim Geom(frac{7}{9})$, but I can't get what is the distribution of Y. What is the pmf of Y? And how to find joint pmf? Thank you.
probability
probability
asked Nov 14 at 5:12
dxdydz
999
asked Nov 14 at 5:12
dxdydz
999
edited Nov 14 at 5:28
asked Nov 14 at 5:12
dxdydz
999
asked Nov 14 at 5:12
dxdydz
999
asked Nov 14 at 5:12
dxdydz
999
999
Events defining $Y$ do not cover whole event space.
– keoxkeox
Nov 14 at 5:25
If the person asking the question is OK with measures not adding up to 1 then $Y sim (4/9) delta(x-1) + (3/9) delta(x-2)$
– keoxkeox
Nov 14 at 5:30
Also your joint pmf will add up to $7/9$
– keoxkeox
Nov 14 at 5:32
add a comment |
Events defining $Y$ do not cover whole event space.
– keoxkeox
Nov 14 at 5:25
If the person asking the question is OK with measures not adding up to 1 then $Y sim (4/9) delta(x-1) + (3/9) delta(x-2)$
– keoxkeox
Nov 14 at 5:30
Also your joint pmf will add up to $7/9$
– keoxkeox
Nov 14 at 5:32
Events defining $Y$ do not cover whole event space.
– keoxkeox
Nov 14 at 5:25
Events defining $Y$ do not cover whole event space.
– keoxkeox
Nov 14 at 5:25
If the person asking the question is OK with measures not adding up to 1 then $Y sim (4/9) delta(x-1) + (3/9) delta(x-2)$
– keoxkeox
Nov 14 at 5:30
If the person asking the question is OK with measures not adding up to 1 then $Y sim (4/9) delta(x-1) + (3/9) delta(x-2)$
– keoxkeox
Nov 14 at 5:30
Also your joint pmf will add up to $7/9$
– keoxkeox
Nov 14 at 5:32
Also your joint pmf will add up to $7/9$
– keoxkeox
Nov 14 at 5:32
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
Guide:
Note thatbegin{align}
Pr(N=n, Y=1) &=left( frac29right)^{n-1}frac{4}{9}
end{align}
Finding $Pr(N=n, Y=2)$ should be similar and you should be able to compute the marginal distribution.
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Guide:
Note thatbegin{align}
Pr(N=n, Y=1) &=left( frac29right)^{n-1}frac{4}{9}
end{align}
Finding $Pr(N=n, Y=2)$ should be similar and you should be able to compute the marginal distribution.
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
add a comment |
up vote
0
down vote
accepted
Guide:
Note thatbegin{align}
Pr(N=n, Y=1) &=left( frac29right)^{n-1}frac{4}{9}
end{align}
Finding $Pr(N=n, Y=2)$ should be similar and you should be able to compute the marginal distribution.
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Guide:
Note thatbegin{align}
Pr(N=n, Y=1) &=left( frac29right)^{n-1}frac{4}{9}
end{align}
Finding $Pr(N=n, Y=2)$ should be similar and you should be able to compute the marginal distribution.
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
Guide:
Note thatbegin{align}
Pr(N=n, Y=1) &=left( frac29right)^{n-1}frac{4}{9}
end{align}
Finding $Pr(N=n, Y=2)$ should be similar and you should be able to compute the marginal distribution.
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
answered Nov 14 at 5:34
Siong Thye Goh
93.9k1462114
93.9k1462114
add a comment |
add a comment |
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Events defining $Y$ do not cover whole event space.
– keoxkeox
Nov 14 at 5:25
If the person asking the question is OK with measures not adding up to 1 then $Y sim (4/9) delta(x-1) + (3/9) delta(x-2)$
– keoxkeox
Nov 14 at 5:30
Also your joint pmf will add up to $7/9$
– keoxkeox
Nov 14 at 5:32