Probability. Solving equation with distribution function
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Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
asked Nov 21 at 8:08
Atstovas
546
|
show 5 more comments
up vote
0
down vote
favorite
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
asked Nov 21 at 8:08
Atstovas
546
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 at 8:33
|
show 5 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
asked Nov 21 at 8:08
Atstovas
546
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
probability probability-theory probability-distributions
asked Nov 21 at 8:08
Atstovas
546
asked Nov 21 at 8:08
Atstovas
546
asked Nov 21 at 8:08
Atstovas
546
asked Nov 21 at 8:08
Atstovas
546
asked Nov 21 at 8:08
Atstovas
546
546
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 at 8:33
|
show 5 more comments
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 at 8:33
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 at 8:25
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 at 8:27
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 at 8:30
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 at 8:33
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 at 8:33
|
show 5 more comments
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Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 at 8:33