Translate and Scale Normal Distribution
$begingroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
$endgroup$
add a comment |
$begingroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
$endgroup$
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
add a comment |
$begingroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
$endgroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
728
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
add a comment |
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
471513
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
471513
$endgroup$
add a comment |
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
471513
$endgroup$
add a comment |
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
471513
$endgroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
471513
answered Dec 3 '18 at 19:00
DineshDinesh
471513
answered Dec 3 '18 at 19:00
DineshDinesh
471513
answered Dec 3 '18 at 19:00
DineshDinesh
471513
471513
add a comment |
add a comment |
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$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54