Course Content
Probability Theory
Probability Theory
3. Conducting Fascinating Experiments
5. Normal Distribution
Calculate Fascinating Probability
Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.
Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x
:
uniform.pdf(x, loc, scale)
.
For calculating the probability of receiving output that is bigger than x
:
uniform.sf(x, loc, scale)
(inclusive).
For calculating the probability of receiving output that is less than x
:
uniform.cdf(x, loc, scale)
(inclusive).
loc
is the lower bound of the distribution (minimum value).scale
is the upper bound of the distribution (maximum value).
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.
Everything was clear?
Calculate Fascinating Probability
Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.
Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x
:
uniform.pdf(x, loc, scale)
.
For calculating the probability of receiving output that is bigger than x
:
uniform.sf(x, loc, scale)
(inclusive).
For calculating the probability of receiving output that is less than x
:
uniform.cdf(x, loc, scale)
(inclusive).
loc
is the lower bound of the distribution (minimum value).scale
is the upper bound of the distribution (maximum value).
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.
Everything was clear?
Calculate Fascinating Probability
Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.
Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x
:
uniform.pdf(x, loc, scale)
.
For calculating the probability of receiving output that is bigger than x
:
uniform.sf(x, loc, scale)
(inclusive).
For calculating the probability of receiving output that is less than x
:
uniform.cdf(x, loc, scale)
(inclusive).
loc
is the lower bound of the distribution (minimum value).scale
is the upper bound of the distribution (maximum value).
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.
Everything was clear?
Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.
Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x
:
uniform.pdf(x, loc, scale)
.
For calculating the probability of receiving output that is bigger than x
:
uniform.sf(x, loc, scale)
(inclusive).
For calculating the probability of receiving output that is less than x
:
uniform.cdf(x, loc, scale)
(inclusive).
loc
is the lower bound of the distribution (minimum value).scale
is the upper bound of the distribution (maximum value).
Task
Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:
- Import
uniform
object. - Calculate the probability that he was born after the
152
nd day of the year (the 1st of June). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year (the 31st of August). With the parameters:- The lower bound is
1
. - The upper bound is
365
.
- The lower bound is
- Calculate the probability that he was born before the
243
rd day of the year and after the152
nd day of the year.