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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 Apr 3 at 12:51
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 Apr 3 at 12:51
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
Apr 3 at 13:07
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
Apr 3 at 13:08
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
Apr 3 at 13:10
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 Apr 3 at 12:51
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 Apr 3 at 12:51
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 Apr 3 at 12:51
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 Apr 3 at 12:51
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 Apr 3 at 12:51
William FluckWilliam Fluck
291
asked Apr 3 at 12:51
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
Apr 3 at 13:07
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
Apr 3 at 13:08
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
Apr 3 at 13:10
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
Apr 3 at 13:07
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
Apr 3 at 13:08
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
Apr 3 at 13:10
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
Apr 3 at 13:07
$begingroup$
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
Apr 3 at 13:07
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
Apr 3 at 13:08
$begingroup$
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
Apr 3 at 13:08
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
Apr 3 at 13:10
$begingroup$
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
Apr 3 at 13:10
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 Apr 3 at 15:44
Richard Hardy
28.1k642128
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
$endgroup$
add a comment |
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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 Apr 3 at 15:44
Richard Hardy
28.1k642128
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
$endgroup$
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 Apr 3 at 15:44
Richard Hardy
28.1k642128
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
$endgroup$
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 Apr 3 at 15:44
Richard Hardy
28.1k642128
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
$endgroup$
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 Apr 3 at 15:44
Richard Hardy
28.1k642128
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
edited Apr 3 at 15:44
Richard Hardy
28.1k642128
edited Apr 3 at 15:44
Richard Hardy
28.1k642128
edited Apr 3 at 15:44
Richard Hardy
28.1k642128
28.1k642128
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
answered Apr 3 at 13:08
Łukasz DeryłoŁukasz Deryło
2,6511417
2,6511417
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
Apr 3 at 13:07
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
Apr 3 at 13:08
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
Apr 3 at 13:10