Why is this random variable Binomial distributed?
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Regarding the following question:
Find the probability that in a group of 20 individuals, there are at
least 3 individuals born in March, given that there is an individual
born in March 20.
The solution marks X as the number of individuals born in march and calculates:
$$ P(Xgeq3 | X geq 1) $$
Claiming that X is binomial distributed. But why?
What is the intuition for that? I though that binomial distribution mostly relates to experiments (like flipping a coin until "heads" shows etc), but for some reason this case doesn't look like an experiment or anything similar.
Thanks!
probability probability-distributions random-variables
asked Nov 24 at 17:07
superuser123
1686
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up vote
0
down vote
favorite
Regarding the following question:
Find the probability that in a group of 20 individuals, there are at
least 3 individuals born in March, given that there is an individual
born in March 20.
The solution marks X as the number of individuals born in march and calculates:
$$ P(Xgeq3 | X geq 1) $$
Claiming that X is binomial distributed. But why?
What is the intuition for that? I though that binomial distribution mostly relates to experiments (like flipping a coin until "heads" shows etc), but for some reason this case doesn't look like an experiment or anything similar.
Thanks!
probability probability-distributions random-variables
asked Nov 24 at 17:07
superuser123
1686
1
If $X_i$ is "the i-th person is born in march, then $X=X_1+...+X_{20}$, i.e. a sum of iid Bernoulli r.v.
– Surb
Nov 24 at 17:10
1
There are only two outcomes, "born in March" and "not born in March." The experiment is to pick a random person, and determine if he was born in March. We perform the experiment $20$ times.
– saulspatz
Nov 24 at 17:52
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Regarding the following question:
Find the probability that in a group of 20 individuals, there are at
least 3 individuals born in March, given that there is an individual
born in March 20.
The solution marks X as the number of individuals born in march and calculates:
$$ P(Xgeq3 | X geq 1) $$
Claiming that X is binomial distributed. But why?
What is the intuition for that? I though that binomial distribution mostly relates to experiments (like flipping a coin until "heads" shows etc), but for some reason this case doesn't look like an experiment or anything similar.
Thanks!
probability probability-distributions random-variables
asked Nov 24 at 17:07
superuser123
1686
Regarding the following question:
Find the probability that in a group of 20 individuals, there are at
least 3 individuals born in March, given that there is an individual
born in March 20.
The solution marks X as the number of individuals born in march and calculates:
$$ P(Xgeq3 | X geq 1) $$
Claiming that X is binomial distributed. But why?
What is the intuition for that? I though that binomial distribution mostly relates to experiments (like flipping a coin until "heads" shows etc), but for some reason this case doesn't look like an experiment or anything similar.
Thanks!
probability probability-distributions random-variables
probability probability-distributions random-variables
asked Nov 24 at 17:07
superuser123
1686
asked Nov 24 at 17:07
superuser123
1686
asked Nov 24 at 17:07
superuser123
1686
asked Nov 24 at 17:07
superuser123
1686
asked Nov 24 at 17:07
superuser123
1686
1686
1
If $X_i$ is "the i-th person is born in march, then $X=X_1+...+X_{20}$, i.e. a sum of iid Bernoulli r.v.
– Surb
Nov 24 at 17:10
1
There are only two outcomes, "born in March" and "not born in March." The experiment is to pick a random person, and determine if he was born in March. We perform the experiment $20$ times.
– saulspatz
Nov 24 at 17:52
add a comment |
1
If $X_i$ is "the i-th person is born in march, then $X=X_1+...+X_{20}$, i.e. a sum of iid Bernoulli r.v.
– Surb
Nov 24 at 17:10
1
There are only two outcomes, "born in March" and "not born in March." The experiment is to pick a random person, and determine if he was born in March. We perform the experiment $20$ times.
– saulspatz
Nov 24 at 17:52
1
1
If $X_i$ is "the i-th person is born in march, then $X=X_1+...+X_{20}$, i.e. a sum of iid Bernoulli r.v.
– Surb
Nov 24 at 17:10
If $X_i$ is "the i-th person is born in march, then $X=X_1+...+X_{20}$, i.e. a sum of iid Bernoulli r.v.
– Surb
Nov 24 at 17:10
1
1
There are only two outcomes, "born in March" and "not born in March." The experiment is to pick a random person, and determine if he was born in March. We perform the experiment $20$ times.
– saulspatz
Nov 24 at 17:52
There are only two outcomes, "born in March" and "not born in March." The experiment is to pick a random person, and determine if he was born in March. We perform the experiment $20$ times.
– saulspatz
Nov 24 at 17:52
add a comment |
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1
If $X_i$ is "the i-th person is born in march, then $X=X_1+...+X_{20}$, i.e. a sum of iid Bernoulli r.v.
– Surb
Nov 24 at 17:10
1
There are only two outcomes, "born in March" and "not born in March." The experiment is to pick a random person, and determine if he was born in March. We perform the experiment $20$ times.
– saulspatz
Nov 24 at 17:52