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 yesterday
Atstovas
334
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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 yesterday
Atstovas
334
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
yesterday
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
yesterday
yes. when x=0 and x=3, jump is 1/5
– Atstovas
yesterday
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
yesterday
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
yesterday
|
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 yesterday
Atstovas
334
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 yesterday
Atstovas
334
asked yesterday
Atstovas
334
asked yesterday
Atstovas
334
asked yesterday
Atstovas
334
asked yesterday
Atstovas
334
334
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
yesterday
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
yesterday
yes. when x=0 and x=3, jump is 1/5
– Atstovas
yesterday
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
yesterday
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
yesterday
|
show 5 more comments
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
yesterday
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
yesterday
yes. when x=0 and x=3, jump is 1/5
– Atstovas
yesterday
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
yesterday
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
yesterday
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
yesterday
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
yesterday
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
yesterday
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
yesterday
yes. when x=0 and x=3, jump is 1/5
– Atstovas
yesterday
yes. when x=0 and x=3, jump is 1/5
– Atstovas
yesterday
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
yesterday
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
yesterday
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
yesterday
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
yesterday
|
show 5 more comments
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Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
yesterday
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
yesterday
yes. when x=0 and x=3, jump is 1/5
– Atstovas
yesterday
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
yesterday
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
yesterday