To find the mean and variance with given conditions
$begingroup$
$X$ follows normal distribution $mathcal{N}(mu , sigma^2)$ with pdf $f$ and cdf $F$. If $max_x f(x)= 0.997356$ and $F(-1)+F(7)=1$, determine $mu, sigma^2$ and $mathbb{P}[Xle 0]$ .
I have no clue about this question and unable to interpret the given conditions. How can I relate the max pdf to find the mean. Even if I get to know the first part I can calculate the rest. Any help would be grateful.
probability-distributions normal-distribution
edited Dec 13 '18 at 12:27
gt6989b
34k22455
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
$endgroup$
add a comment |
$begingroup$
$X$ follows normal distribution $mathcal{N}(mu , sigma^2)$ with pdf $f$ and cdf $F$. If $max_x f(x)= 0.997356$ and $F(-1)+F(7)=1$, determine $mu, sigma^2$ and $mathbb{P}[Xle 0]$ .
I have no clue about this question and unable to interpret the given conditions. How can I relate the max pdf to find the mean. Even if I get to know the first part I can calculate the rest. Any help would be grateful.
probability-distributions normal-distribution
edited Dec 13 '18 at 12:27
gt6989b
34k22455
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
$endgroup$
add a comment |
$begingroup$
$X$ follows normal distribution $mathcal{N}(mu , sigma^2)$ with pdf $f$ and cdf $F$. If $max_x f(x)= 0.997356$ and $F(-1)+F(7)=1$, determine $mu, sigma^2$ and $mathbb{P}[Xle 0]$ .
I have no clue about this question and unable to interpret the given conditions. How can I relate the max pdf to find the mean. Even if I get to know the first part I can calculate the rest. Any help would be grateful.
probability-distributions normal-distribution
edited Dec 13 '18 at 12:27
gt6989b
34k22455
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
$endgroup$
$X$ follows normal distribution $mathcal{N}(mu , sigma^2)$ with pdf $f$ and cdf $F$. If $max_x f(x)= 0.997356$ and $F(-1)+F(7)=1$, determine $mu, sigma^2$ and $mathbb{P}[Xle 0]$ .
I have no clue about this question and unable to interpret the given conditions. How can I relate the max pdf to find the mean. Even if I get to know the first part I can calculate the rest. Any help would be grateful.
probability-distributions normal-distribution
probability-distributions normal-distribution
edited Dec 13 '18 at 12:27
gt6989b
34k22455
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
edited Dec 13 '18 at 12:27
gt6989b
34k22455
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
edited Dec 13 '18 at 12:27
gt6989b
34k22455
edited Dec 13 '18 at 12:27
gt6989b
34k22455
edited Dec 13 '18 at 12:27
gt6989b
34k22455
34k22455
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
asked Dec 13 '18 at 12:20
Kriti AroraKriti Arora
396
396
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
HINT
Since $X sim mathcal{N}left(mu,sigma^2right)$, you know that
$$
f(x) = frac{1}{sigma sqrt{2pi}}
expleft(frac{-1}{2} left(frac{x-mu}{sigma} right)^2 right)
$$
which is the bell curve, clearly reaching maximum at $x = mu$. What is this maximum, and can you find $sigma$ from its value?
Then use the fact that $(X-mu)/sigma sim mathcal{N}(0,1)$ and usual relationship of the std normal cdf to figure out $mu$ from the second relation.
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
$endgroup$
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
$begingroup$
HINT
Since $X sim mathcal{N}left(mu,sigma^2right)$, you know that
$$
f(x) = frac{1}{sigma sqrt{2pi}}
expleft(frac{-1}{2} left(frac{x-mu}{sigma} right)^2 right)
$$
which is the bell curve, clearly reaching maximum at $x = mu$. What is this maximum, and can you find $sigma$ from its value?
Then use the fact that $(X-mu)/sigma sim mathcal{N}(0,1)$ and usual relationship of the std normal cdf to figure out $mu$ from the second relation.
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
$endgroup$
add a comment |
$begingroup$
HINT
Since $X sim mathcal{N}left(mu,sigma^2right)$, you know that
$$
f(x) = frac{1}{sigma sqrt{2pi}}
expleft(frac{-1}{2} left(frac{x-mu}{sigma} right)^2 right)
$$
which is the bell curve, clearly reaching maximum at $x = mu$. What is this maximum, and can you find $sigma$ from its value?
Then use the fact that $(X-mu)/sigma sim mathcal{N}(0,1)$ and usual relationship of the std normal cdf to figure out $mu$ from the second relation.
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
$endgroup$
add a comment |
$begingroup$
HINT
Since $X sim mathcal{N}left(mu,sigma^2right)$, you know that
$$
f(x) = frac{1}{sigma sqrt{2pi}}
expleft(frac{-1}{2} left(frac{x-mu}{sigma} right)^2 right)
$$
which is the bell curve, clearly reaching maximum at $x = mu$. What is this maximum, and can you find $sigma$ from its value?
Then use the fact that $(X-mu)/sigma sim mathcal{N}(0,1)$ and usual relationship of the std normal cdf to figure out $mu$ from the second relation.
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
$endgroup$
HINT
Since $X sim mathcal{N}left(mu,sigma^2right)$, you know that
$$
f(x) = frac{1}{sigma sqrt{2pi}}
expleft(frac{-1}{2} left(frac{x-mu}{sigma} right)^2 right)
$$
which is the bell curve, clearly reaching maximum at $x = mu$. What is this maximum, and can you find $sigma$ from its value?
Then use the fact that $(X-mu)/sigma sim mathcal{N}(0,1)$ and usual relationship of the std normal cdf to figure out $mu$ from the second relation.
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
answered Dec 13 '18 at 12:25
gt6989bgt6989b
34k22455
34k22455
add a comment |
add a comment |
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