Question

Probability density function http://prntscr.com/5h05ti

Answer 1

@ganeshie8

Answer 2

sum of pdf is always 1, right?

Answer 3

\[1 = \sum_{x=0}^\infty k\left(\dfrac{4}{5}\right)^x = k\sum_{x=0}^\infty \left(\dfrac{4}{5}\right)^x\]

So \(\displaystyle \dfrac{1}{\displaystyle \sum_{x=0}^\infty \left(\dfrac{4}{5}\right)^x} = k\).

you can solve sum using the fact that \(\displaystyle \sum_{x=0}^\infty r^x = \dfrac{1}{1-r}\) (if i remember correctly lol)

Answer 4

does that help? @junyang96

Answer 5

oh I see. I totally forgot the sum to infinity formula. Thanks