Question 1164546
<pre>
This concerns getting the probablity that we will get our first success on the
kth trial, with a probability of success on each trial being p = 1/3.

The other tutor was correct for part b), which was: 

b)
{{{E(X)=1/p=(1^"")/(1/3)=3}}}
{{{Var(X)=((1-p)/p^2)=(2/3)/(1/9)=(2/3)*9=2*3=6}}}

a) Instead of plotting, I'll just list the values:
PMF(probability mass function) {{{P(X=k)=(1-p)^(k-1)*p}}}
CDF(cumulative distribution function) {{{P(X<=k)=1-(1-p)^k}}}

 k|PMF(k) |CDF(k)
 1|0.3333 |0.3333    
 2|0.2222 |0.5556
 3|0.1481 |0.7037
 4|0.0988 |0.8025
 5|0.0658 |0.8683
 6|0.0439 |0.9122
 7|0.0293 |0.9415
 8|0.0195 |0.9610
 9|0.0130 |0.9740
10|0.0087 |0.9827

c)
{{{P(X>k)=(1-p)^k}}}  
{{{P(X>4)=(1-1/3)^4=(2/3)^4=(2/3)^4=16/81=0.1975}}} (approximately)
 
Edwin</pre>