pmf vs binomial distribution vs cdf

[Doom]

Hi,
I have confusion of probability mass function. Is there any difference among pmf, binomial distribution and cdf for discrete random variables? The pmf seems to be the same as binomial distribution or cdf when calculating the probability in any related problems as I see from the textbook.

 

[BigBeachBanana]

Hi,
I have confusion of probability mass function. Is there any difference among pmf, binomial distribution and cdf for discrete random variables? The pmf seems to be the same as binomial distribution or cdf when calculating the probability in any related problems as I see from the textbook.

Yes, there's a difference.

The PMF of a binomial distribution is
\(\displaystyle \Pr(X=k)={n \choose k}p^k(1-p)^{n-k}\)

Whereas the CDF is cumulative of the PMF.
\(\displaystyle \Pr(X\le k)=\sum_{i=0}^k{n \choose i}p^i(1-p)^{n-i}\)

 

[Dr.Peterson]

Hi,
I have confusion of probability mass function. Is there any difference among pmf, binomial distribution and cdf for discrete random variables? The pmf seems to be the same as binomial distribution or cdf when calculating the probability in any related problems as I see from the textbook.

It may help if you show us what the book says that you see as being the same, so we can identify any misunderstandings you have.

 

[Doom]

Yes, there's a difference.

The PMF of a binomial distribution is
\(\displaystyle \Pr(X=k)={n \choose k}p^k(1-p)^{n-k}\)

Whereas the CDF is cumulative of the PMF.
\(\displaystyle \Pr(X\le k)=\sum_{i=0}^k{n \choose i}p^i(1-p)^{n-i}\)

Thanks for listing the formula to compare, it's very helpful.

 

[Doom]

It may help if you show us what the book says that you see as being the same, so we can identify any misunderstandings you have.

Thank you! The section of that book is related to the probability of a specific random variable value. After reading the book furthermore, I see the difference between them.