6. Statistics and Probability

Discrete Distributions — Quiz

Test your understanding of discrete distributions with 5 practice questions.

Practice Questions

Question 1

A discrete random variable $X$ has a probability mass function given by $P(X=x) = c(x+1)$ for $x=0, 1, 2, 3$. What is the value of the constant $c$?

Question 2

A company manufactures electronic components, and it is known that $3\%$ of the components are defective. If a random sample of 20 components is selected, what is the probability that at least 2 components are defective? (Round to 4 decimal places)

Question 3

A discrete random variable $X$ has an expected value $E(X) = 2.5$ and $E(X^2) = 7.25$. What is the variance $Var(X)$?

Question 4

In a binomial distribution, if the mean is 4.8 and the variance is 2.88, what are the values of $n$ (number of trials) and $p$ (probability of success)?

Question 5

A game involves rolling a biased six-sided die where the probability of rolling a '6' is $0.3$. If the die is rolled 5 times, what is the probability of rolling at least one '6'?