3. Discrete Random Variables

Binomial Distribution — Quiz

Test your understanding of binomial distribution with 5 practice questions.

Practice Questions

Question 1

If $X\sim\mathrm{Bin}(n,p)$ and $Y=n-X$, what is the distribution of $Y$?

Question 2

For $X\sim\mathrm{Bin}(12,0.25)$, what is $P(X=3)$?

Question 3

For $X\sim\mathrm{Bin}(10,0.3)$, what is $P(2\le X\le4)$?

Question 4

A biased die has $P(6)=\tfrac13$ and is rolled 9 times. If $X$ is the number of sixes, what are $E[X]$ and $\mathrm{Var}(X)$?

Question 5

If a binomial random variable has $E[X]=8$ and $\mathrm{Var}(X)=4$, find $n$ and $p$.