Theory test: Probability and statistics

6 questions. Pass with 5 correct.

1. 01 What is the expected value of a fair six-sided die?

   33.546
2. 02 If $\mathrm{Var}(X)=5$, what is $\mathrm{Var}(2X)$?

   5102025
3. 03 Prevalence 1%, sensitivity 90%, false-positive rate 9%. Roughly what is $P(\text{sick}\mid \text{positive})$?

   90%50%9%1%
4. 04 A coin lands heads 7 times in 10 flips. What is the maximum likelihood estimate of $P(\text{heads})$?

   0.50.70.3It can't be estimated from 10 flips
5. 05 A model's errors have $\sigma =10$. What is the standard error of their average over $n=100$ examples?

   0.1110100
6. 06 Two variables have correlation 0. Which is true?

   They are independentThere is no linear relationship, but there could be a non-linear oneOne causes the otherTheir variances are equal