Set 2: Statistics

Welcome to the second set!

5 questions: 30min.

Theme: statistics, all questions from statistics. These are from basic statistics for everyone, no specialised knowledge required. Suitable for the general person.

Focus! Block out distractions! Your time will NOT be taken into account when measuring your $\text{iq}^\ell$. You can take all of it or less, once you think you are done, you can’t edit anymore. So, finishing early gives you nothing.

Good luck! :)

No. 1

If $X \sim \text{Bern}(p, 1-p)$ does it mean that $X$ models a fair coin toss?

If it is coin toss, fair or not, what is the smallest $p$ can be? Explain?

No. 2

Suppose you sample $X_1,. . . ,X_n$ from a population of mice. You obtain $\bar{X}$ for an average of the quantity you wanted.

Does a positive value of $\bar{X}$ mean that the sample has all positive values?

No. 3

The sides of a right triangle are random. At most, how many could be random by themselves? That is, how many can change independently of each other?

No. 4

Two people have a birthday today. What’s the chance they will have it on the same day again? It is Saturday today. No leap years.

No. 5

Charlie brought a peanut butter sandwich to work and the staff became jealous. He said he would give half of it to whichever person can roll, using 2 6 sided dice, the product as 13.

What’s the chance of this happening?

That’s the end of the second set. Hope you did well!