Recent questions in Types of Bias

Types of Bias
Answered

Sandra Terrell
2022-08-10

Now say I can observe $C$ and want to figure out if the coin was heads or tails, i.e. I want to compute $Pr[$

One thought I had was to approximate the coin toss with a continuous random variable $K$ with pdf:

$k(x)=b,{\textstyle \text{for}}x\in [-1,0]$

$k(x)=1-b,{\textstyle \text{for}}x\in [0,1]$

Then one could compute the joint density function for $K$ and $C$ and compute $Pr[K<0|C=c]$ from there. But this looks clunky and ugly. Is there a better way?

Types of Bias
Answered

Brenton Dixon
2022-07-21

$6$ normal dice. The probability to get a $6$ is $1/6$ for each dice.

$3$ biased dice. The probability to get a $6$ is $0.85$.$3$ biased dice. The probability to get a $6$ is $0.05$.You take a die from the box at random and roll it.What is the conditional probability that it is of type $b$, given that it gives a $6$?