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Probability that a draw from a normal distribution is some number greater than another draw from the same distribution
Probability that two random letters from a language will be the same?Comparing two probabilities from the same normal distributionProbability of rolling one die by two persons 3 times each, and problem with pulling out cardsGiven a draw from one of two overlapping normal distributions, what is the probability it came from one vs. the other?Given a draw from some normal distribution, what is the distribution of your beliefs about its mean?What is the probability of having at least X values greater than 0 given an n-dimensional multivariate normal distribution?Calculate probability that mean of one distribution is greater than mean of another distribution with normal-gamma priors on each meanLikelihood that one group of survery takers has a mean greater than another group with differing distributionsHow do I estimate the p-value for the null hypothesis that these two sets of values have the same probability of falling within a specific range?obtaining a distribution from the sum of normal distributions
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I hope to learn the general way of solving this problem, but I have this specific problem:
$$
Xsim N(mu,sigma^2) \
mu=470, sigma=70
$$
If two people, A and B, each draw one entry from the same distribution, what is the probability that A's entry is at least 100 more than B's entry?
probability distributions normal-distribution
asked yesterday
William FluckWilliam Fluck
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I hope to learn the general way of solving this problem, but I have this specific problem:
$$
Xsim N(mu,sigma^2) \
mu=470, sigma=70
$$
If two people, A and B, each draw one entry from the same distribution, what is the probability that A's entry is at least 100 more than B's entry?
probability distributions normal-distribution
asked yesterday
William FluckWilliam Fluck
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Let $A$ and $B$ be two independent random variables both with distribution $mathcalN(mu, sigma^2)$. What is the distribution of the random variable $A-B$?
$endgroup$
– olooney
yesterday
1
$begingroup$
You have $A-B>100$. Rearrange to $A-B-100>0$. Now all you have to do is figuring out the distribution of $A-B-100$. In this case, this is quite easy (hint: it's still a normal distribution).
$endgroup$
– COOLSerdash
yesterday
1
$begingroup$
Hint: $A-B$ is also a normal random variable. Can you figure out what the mean and variance of $A-B$ are? If so, you should be able to answer the question; What is the probability that $A-B$ is $100$ or more?
$endgroup$
– Dilip Sarwate
yesterday
add a comment |
$begingroup$
I hope to learn the general way of solving this problem, but I have this specific problem:
$$
Xsim N(mu,sigma^2) \
mu=470, sigma=70
$$
If two people, A and B, each draw one entry from the same distribution, what is the probability that A's entry is at least 100 more than B's entry?
probability distributions normal-distribution
asked yesterday
William FluckWilliam Fluck
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I hope to learn the general way of solving this problem, but I have this specific problem:
$$
Xsim N(mu,sigma^2) \
mu=470, sigma=70
$$
If two people, A and B, each draw one entry from the same distribution, what is the probability that A's entry is at least 100 more than B's entry?
probability distributions normal-distribution
probability distributions normal-distribution
asked yesterday
William FluckWilliam Fluck
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
William FluckWilliam Fluck
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
William FluckWilliam Fluck
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
William FluckWilliam Fluck
291
asked yesterday
William FluckWilliam Fluck
291
291
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
William Fluck is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Let $A$ and $B$ be two independent random variables both with distribution $mathcalN(mu, sigma^2)$. What is the distribution of the random variable $A-B$?
$endgroup$
– olooney
yesterday
1
$begingroup$
You have $A-B>100$. Rearrange to $A-B-100>0$. Now all you have to do is figuring out the distribution of $A-B-100$. In this case, this is quite easy (hint: it's still a normal distribution).
$endgroup$
– COOLSerdash
yesterday
1
$begingroup$
Hint: $A-B$ is also a normal random variable. Can you figure out what the mean and variance of $A-B$ are? If so, you should be able to answer the question; What is the probability that $A-B$ is $100$ or more?
$endgroup$
– Dilip Sarwate
yesterday
add a comment |
1
$begingroup$
Let $A$ and $B$ be two independent random variables both with distribution $mathcalN(mu, sigma^2)$. What is the distribution of the random variable $A-B$?
$endgroup$
– olooney
yesterday
1
$begingroup$
You have $A-B>100$. Rearrange to $A-B-100>0$. Now all you have to do is figuring out the distribution of $A-B-100$. In this case, this is quite easy (hint: it's still a normal distribution).
$endgroup$
– COOLSerdash
yesterday
1
$begingroup$
Hint: $A-B$ is also a normal random variable. Can you figure out what the mean and variance of $A-B$ are? If so, you should be able to answer the question; What is the probability that $A-B$ is $100$ or more?
$endgroup$
– Dilip Sarwate
yesterday
1
1
$begingroup$
Let $A$ and $B$ be two independent random variables both with distribution $mathcalN(mu, sigma^2)$. What is the distribution of the random variable $A-B$?
$endgroup$
– olooney
yesterday
$begingroup$
Let $A$ and $B$ be two independent random variables both with distribution $mathcalN(mu, sigma^2)$. What is the distribution of the random variable $A-B$?
$endgroup$
– olooney
yesterday
1
1
$begingroup$
You have $A-B>100$. Rearrange to $A-B-100>0$. Now all you have to do is figuring out the distribution of $A-B-100$. In this case, this is quite easy (hint: it's still a normal distribution).
$endgroup$
– COOLSerdash
yesterday
$begingroup$
You have $A-B>100$. Rearrange to $A-B-100>0$. Now all you have to do is figuring out the distribution of $A-B-100$. In this case, this is quite easy (hint: it's still a normal distribution).
$endgroup$
– COOLSerdash
yesterday
1
1
$begingroup$
Hint: $A-B$ is also a normal random variable. Can you figure out what the mean and variance of $A-B$ are? If so, you should be able to answer the question; What is the probability that $A-B$ is $100$ or more?
$endgroup$
– Dilip Sarwate
yesterday
$begingroup$
Hint: $A-B$ is also a normal random variable. Can you figure out what the mean and variance of $A-B$ are? If so, you should be able to answer the question; What is the probability that $A-B$ is $100$ or more?
$endgroup$
– Dilip Sarwate
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Since it looks like self-study question, I'll start with a hint: Think of $X_1-X_2$ with
$X_1, X_2 sim N(470, 70^2)$. What distribution does $X_1-X_2$ follow? How to interpret $X_1-X_2$?
edited yesterday
Richard Hardy
28.1k642128
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Since it looks like self-study question, I'll start with a hint: Think of $X_1-X_2$ with
$X_1, X_2 sim N(470, 70^2)$. What distribution does $X_1-X_2$ follow? How to interpret $X_1-X_2$?
edited yesterday
Richard Hardy
28.1k642128
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
$endgroup$
add a comment |
$begingroup$
Since it looks like self-study question, I'll start with a hint: Think of $X_1-X_2$ with
$X_1, X_2 sim N(470, 70^2)$. What distribution does $X_1-X_2$ follow? How to interpret $X_1-X_2$?
edited yesterday
Richard Hardy
28.1k642128
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
$endgroup$
add a comment |
$begingroup$
Since it looks like self-study question, I'll start with a hint: Think of $X_1-X_2$ with
$X_1, X_2 sim N(470, 70^2)$. What distribution does $X_1-X_2$ follow? How to interpret $X_1-X_2$?
edited yesterday
Richard Hardy
28.1k642128
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
$endgroup$
Since it looks like self-study question, I'll start with a hint: Think of $X_1-X_2$ with
$X_1, X_2 sim N(470, 70^2)$. What distribution does $X_1-X_2$ follow? How to interpret $X_1-X_2$?
edited yesterday
Richard Hardy
28.1k642128
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
edited yesterday
Richard Hardy
28.1k642128
edited yesterday
Richard Hardy
28.1k642128
edited yesterday
Richard Hardy
28.1k642128
28.1k642128
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
answered yesterday
Łukasz DeryłoŁukasz Deryło
2,6361417
2,6361417
add a comment |
add a comment |
William Fluck is a new contributor. Be nice, and check out our Code of Conduct.
William Fluck is a new contributor. Be nice, and check out our Code of Conduct.
William Fluck is a new contributor. Be nice, and check out our Code of Conduct.
William Fluck is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
Let $A$ and $B$ be two independent random variables both with distribution $mathcalN(mu, sigma^2)$. What is the distribution of the random variable $A-B$?
$endgroup$
– olooney
yesterday
1
$begingroup$
You have $A-B>100$. Rearrange to $A-B-100>0$. Now all you have to do is figuring out the distribution of $A-B-100$. In this case, this is quite easy (hint: it's still a normal distribution).
$endgroup$
– COOLSerdash
yesterday
1
$begingroup$
Hint: $A-B$ is also a normal random variable. Can you figure out what the mean and variance of $A-B$ are? If so, you should be able to answer the question; What is the probability that $A-B$ is $100$ or more?
$endgroup$
– Dilip Sarwate
yesterday