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Simplifying probablity equation based on its cumulative distribution function (CDF)
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1
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How can I simplify the following probability equation based on cumulative distribution function of X:
P(X>a)>b
which P is the probability of X and X has a known probability distribution function and a & b are real positive numbers.
probability probability-distributions
edited Aug 1 at 15:26
BCLC
7,01221973
asked Jul 31 at 14:44
Dastnegar Parseh
124
add a comment |Â
up vote
1
down vote
favorite
How can I simplify the following probability equation based on cumulative distribution function of X:
P(X>a)>b
which P is the probability of X and X has a known probability distribution function and a & b are real positive numbers.
probability probability-distributions
edited Aug 1 at 15:26
BCLC
7,01221973
asked Jul 31 at 14:44
Dastnegar Parseh
124
1
Do you the definition of a CDF?
– user190080
Jul 31 at 14:48
Back to the problem: Start with $X$ has cdf $F_X(X le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'.
– BruceET
Aug 1 at 4:40
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
How can I simplify the following probability equation based on cumulative distribution function of X:
P(X>a)>b
which P is the probability of X and X has a known probability distribution function and a & b are real positive numbers.
probability probability-distributions
edited Aug 1 at 15:26
BCLC
7,01221973
asked Jul 31 at 14:44
Dastnegar Parseh
124
How can I simplify the following probability equation based on cumulative distribution function of X:
P(X>a)>b
which P is the probability of X and X has a known probability distribution function and a & b are real positive numbers.
probability probability-distributions
edited Aug 1 at 15:26
BCLC
7,01221973
asked Jul 31 at 14:44
Dastnegar Parseh
124
edited Aug 1 at 15:26
BCLC
7,01221973
edited Aug 1 at 15:26
BCLC
7,01221973
edited Aug 1 at 15:26
BCLC
7,01221973
7,01221973
asked Jul 31 at 14:44
Dastnegar Parseh
124
asked Jul 31 at 14:44
Dastnegar Parseh
124
asked Jul 31 at 14:44
Dastnegar Parseh
124
124
1
Do you the definition of a CDF?
– user190080
Jul 31 at 14:48
Back to the problem: Start with $X$ has cdf $F_X(X le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'.
– BruceET
Aug 1 at 4:40
add a comment |Â
1
Do you the definition of a CDF?
– user190080
Jul 31 at 14:48
Back to the problem: Start with $X$ has cdf $F_X(X le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'.
– BruceET
Aug 1 at 4:40
1
1
Do you the definition of a CDF?
– user190080
Jul 31 at 14:48
Do you the definition of a CDF?
– user190080
Jul 31 at 14:48
Back to the problem: Start with $X$ has cdf $F_X(X le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'.
– BruceET
Aug 1 at 4:40
Back to the problem: Start with $X$ has cdf $F_X(X le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'.
– BruceET
Aug 1 at 4:40
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
$$P(X>a)>b$$
$$-P(X>a)<-b$$
$$1-P(X>a)<1-b$$
$$P(X le a)<1-b$$
$$F_X(a)<1-b$$
answered Aug 1 at 5:20
BCLC
7,01221973
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
$$P(X>a)>b$$
$$-P(X>a)<-b$$
$$1-P(X>a)<1-b$$
$$P(X le a)<1-b$$
$$F_X(a)<1-b$$
answered Aug 1 at 5:20
BCLC
7,01221973
add a comment |Â
up vote
1
down vote
$$P(X>a)>b$$
$$-P(X>a)<-b$$
$$1-P(X>a)<1-b$$
$$P(X le a)<1-b$$
$$F_X(a)<1-b$$
answered Aug 1 at 5:20
BCLC
7,01221973
add a comment |Â
up vote
1
down vote
up vote
1
down vote
$$P(X>a)>b$$
$$-P(X>a)<-b$$
$$1-P(X>a)<1-b$$
$$P(X le a)<1-b$$
$$F_X(a)<1-b$$
answered Aug 1 at 5:20
BCLC
7,01221973
$$P(X>a)>b$$
$$-P(X>a)<-b$$
$$1-P(X>a)<1-b$$
$$P(X le a)<1-b$$
$$F_X(a)<1-b$$
answered Aug 1 at 5:20
BCLC
7,01221973
answered Aug 1 at 5:20
BCLC
7,01221973
answered Aug 1 at 5:20
BCLC
7,01221973
answered Aug 1 at 5:20
BCLC
7,01221973
7,01221973
add a comment |Â
add a comment |Â
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1
Do you the definition of a CDF?
– user190080
Jul 31 at 14:48
Back to the problem: Start with $X$ has cdf $F_X(X le a) = 1 - P(X > a).$ You can get other, possibly useful, relationships from there. Not sure whether I'd call the 'simplifications'.
– BruceET
Aug 1 at 4:40