We are going to play a simple game. We start with 0 points. We will flip a coin. If it comes up heads, we get two points. If comes up tails, we double our current score.
For example,
if we got HTH, we would have ((0+2)∗2+2)=6 points, but if we got THT, we would have ((0)∗2+2)∗2=4 points. Report all answers using 6 digits of precision.
Questions to be answered:

We’ll play the game with an unfair coin. It has a 70% chance of coming up heads. What is our expected score after 20 flips?

What is the standard deviation?