Consider a coin that comes up heads with probability 1/7 and comes up tails with probability 6/7.
You flip this coin once. If it comes up heads, you win \$5. If it comes up tails, you win \$2.
What is the expected value $\mathbb{E}(X)$ of $X$?
(a)
17/7
(b)
7/17
(c)
7/2
(d)
32/7
Solution
Let's determine X=5
The probability of getting heads is $ \frac{1}{7} $
$ Pr(X=5) = \frac{1}{7} $
Let's determine X=2
The probability of getting tails is $ \frac{6}{7} $
$ Pr(X=2) = \frac{6}{7} $