# Thread: Simple question on probability.

1. ## Simple question on probability.

Alright... i am new to this forum...this may seems quite easy for you guys... but i've been very confused lately

What is the maximum probability value that a cumulative density function (cdf) can have?

Now i know that a probability can have a event of 0 to 1... asking for maximum probability i assume it will be 1? But then thinking again.. when it relates to CDF (which i don't fully understand) it can be limited to (.5) or even to infinite?

2. Originally Posted by holymackerel
Alright... i am new to this forum...this may seems quite easy for you guys... but i've been very confused lately

What is the maximum probability value that a cumulative density function (cdf) can have?

Now i know that a probability can have a event of 0 to 1... asking for maximum probability i assume it will be 1? But then thinking again.. when it relates to CDF (which i don't fully understand) it can be limited to (.5) or even to infinite?

Do you understand that the cdf F(x) is an increasing function such that $\lim_{x \rightarrow +\infty} F(x) = 1$ .....?

3. let me give an example
to be simple let consider a discret example
F(x) is P(X<=x)
like a F(5) is a sum i=0 to 5 of P(X=i) considering the X assumes values 0 to i infinte let's say

so like u said the probability assumes values between 0 to 1 so the max of a F is the sum of all probabilites in all points and that's 1 by definition

4. so i was right that the max value is 1? i keep getting confuse with the CFD's parameters as it says x to infinite...

which leads me to my next questions... that any random variable with a normal distribution can be converted to a random variable with a standard normal distribution? or am i wrong?

and thanks for the prompt replies... you guys are great... helping an unknown fellow.. really appreciate it.

5. Originally Posted by holymackerel
so i was right that the max value is 1? i keep getting confuse with the CFD's parameters as it says x to infinite...

which leads me to my next questions... that any random variable with a normal distribution can be converted to a random variable with a standard normal distribution? or am i wrong?

and thanks for the prompt replies... you guys are great... helping an unknown fellow.. really appreciate it.
$Z = \frac{X - \mu}{\sigma}$

where X ~ Normal( $\mu, \, \sigma$) and Z ~ Normal (0, 1).

6. ok i was wrong... thanks =)

7. Originally Posted by holymackerel
ok i was wrong... thanks =)
No. You're right. I gave the conversion ......

8. excellent, thanks again. i have to admit that probability is my weakest subject... as it's the most worded topic there is. i shall be back for further enquiries...