5. Statistics and Probability
Discrete Distributions — Quiz
Test your understanding of discrete distributions with 5 practice questions.
Practice Questions
Question 1
A biased coin has a probability of landing heads as $0.6$. If the coin is flipped 4 times, what is the probability of getting exactly 3 heads?
Question 2
A company's quality control department finds that $5\%$ of the items produced are defective. If items are inspected one by one, what is the probability that the first defective item is found on the 2nd inspection?
Question 3
A discrete random variable $X$ has the following probability distribution:
| $x$ | $P(X=x)$ |
|---|---|
| 0 | $0.1$ |
| 1 | $0.2$ |
| 2 | $0.3$ |
| 3 | $0.4$ |
What is the variance $Var(X)$?
| $x$ | $P(X=x)$ |
|---|---|
| 0 | $0.1$ |
| 1 | $0.2$ |
| 2 | $0.3$ |
| 3 | $0.4$ |
What is the variance $Var(X)$?
Question 4
In a binomial distribution, if the number of trials $n=10$ and the probability of success $p=0.3$, what is the probability of getting at most 1 success?
Question 5
A student takes a multiple-choice test with 15 questions. Each question has 4 options, and only one is correct. If the student guesses randomly on all questions, what is the standard deviation of the number of correct answers?