(Old midterms provided by prof to study)
I'm struggling to figure out question 9.
My best guess it that it's all the combined probabilities added together before P(X=6), so: 1 - 0.13 = 0.87. But, as the student who took it got it wrong, I'm not sure. Can someone let me know if I'm right?
If 0.87 is wrong, my other guess is that it would be 0.2 * 5, so 1.
Thanks!
The notation used by the professor for the cumulative distribution function, $$F(X = 5),$$ is very strange and not standard practice in probability theory or statistics. It is far more common to write $$F_X(5)$$ which is equivalent to $$\Pr[X \le 5],$$ the probability that $X$ is at most $5$. The notation $$P(X = 4)$$ is common, in fact, more common than the equivalent $\Pr[X = 4]$ which is my personal preference.
Regarding the answer itself, it is obvious that $$F(X = 5) = F_X(5) = \Pr[X \le 5] = 1 - \Pr[X = 6] = 1 - 0.13 = 0.87.$$ This is because we are given the complete probability mass function for $X$ and the event $X \le 5$ is complementary to $X = 6$.