CDF - Cumulative Density Function

[nasi112]

if i have a CDF

[MATH] F(x) = \begin{cases} 0, & x < 0 \\ \frac{x}{4}, & 0\leq x < 1 \\ \frac{1}{2}, & 1 \leq x < 2 \\ \frac{x}{12} + \frac{1}{2}, & 2 \leq x < 3 \\ 1, & x \geq 3 \end{cases} [/MATH]
Find [math]F(x = 1.6)[/math] and [math]p(x = 1.6)[/math]
it is clear that [MATH]F(1.6) = \frac{1}{2}[/MATH]
but what about [MATH]p(x = 1.6)[/MATH]?

 

[Deleted member 4993]

if i have a CDF

[MATH] F(x) = \begin{cases} 0, & x < 0 \\ \frac{x}{4}, & 0\leq x < 1 \\ \frac{1}{2}, & 1 \leq x < 2 \\ \frac{x}{12} + \frac{1}{2}, & 2 \leq x < 3 \\ 1, & x \geq 3 \end{cases} [/MATH]
Find [math]F(x = 1.6)[/math] and [math]p(x = 1.6)[/math]
it is clear that [MATH]F(1.6) = \frac{1}{2}[/MATH]
but what about [MATH]p(x = 1.6)[/MATH]?

What is the relationship between F and P?

 

[nasi112]

if you have one function, you can get the other. But the CDF has variables such as [MATH]\frac{x}{4}[/MATH]. Therefore, I cannot get its PMF.

 

[Harry_the_cat]

if you have one function, you can get the other. But the CDF has variables such as [MATH]\frac{x}{4}[/MATH]. Therefore, I cannot get its PMF.

How do you get one from the other?

 

[nasi112]

for example

[MATH]p(3) = 1 - \left(\frac{x}{12} + \frac{1}{2} \right)[/MATH]

 

[Deleted member 4993]

for example

[MATH]p(3) = 1 - \left(\frac{x}{12} + \frac{1}{2} \right)[/MATH]

What would be the. CDF in that case?

 

[nasi112]

What?

 

[Deleted member 4993]

What?

Sorry about that typo - fixed it.

 

[nasi112]

CDF is already given.

Do you mean what would be the PMF?

 

[Deleted member 4993]

NO!

for example

[MATH]p(3) = 1 - \left(\frac{x}{12} + \frac{1}{2} \right)[/MATH]

What was the CDF in this case!

 

[nasi112]

I am sorry. I cannot get you.

if you do complete all of them, you will notice that

p(0) + p(1) + p(2) + p(3) [MATH]\neq 1[/MATH]
then PMF will not be fair