Question 1

A random variable $$X is $$defined as the number of tails when tossing three coins. What is the probability that $$X = 2$$?

Accepted Answer

$$\frac{3}{8}$$

Question 2

Which of the following is NOT a property of a binomial distribution?

Accepted Answer

The probability of success changes from trial to trial.

Question 3

Suppose a factory produces 2 defective units per day on average. What is the probability that there are no defectives on a given day? (Use the Poisson distribution)

Accepted Answer

$$e^{-2}$$

Question 4

If $$X is a $$discrete random variable with probability distribution $$P(X=x)$$, which formula gives the expected value $$E(X)$$?

Accepted Answer

$$E(X) = \sum_x x P(X=x)$$

Question 5

A call center receives calls at a rate of 3 per minute. What is the probability that exactly 2 calls arrive in one minute? (Poisson distribution)

Accepted Answer

$$e^{-3}$$ \frac{$$3^2$$}{2!}$$

Question 6

Which of the following is a characteristic of a discrete random variable?

Accepted Answer

It can only take on whole number values.

Question 7

A Bernoulli random variable $$X$$ has $$P(X=1) = 0.01. $$What is $$P(X=0)$$?

Accepted Answer

0.99

Question 8

If $$X is a $$binomial random variable with $$n=5$$ and $$p=0.1$$, what is the probability that none are left-handed in a sample of 5 people?

Accepted Answer

$$(1-0.1)^5$$

Question 9

Which formula correctly gives the variance of a binomial random variable $$X$$ with parameters $$n$$ and $$p$$?

Accepted Answer

$$Var(X) = np(1-p)$$

Question 10

A random variable $$X$$ has the following probability distribution: $$P(X=0)=0.25$$, $$P(X=1)=0.5$$, $$P(X=2)=0.25. $$What is $$E(X)$$?

Accepted Answer

$$1$$

Question 11

Which of the following scenarios is best modeled by a Poisson distribution?

Accepted Answer

The number of emails received per hour.

Question 12

If $$X is a $$binomial random variable with $$n=8$$ and $$p=0.6$$, what is $$E(X)$$?

Accepted Answer

$$4.8$$

Question 13

A random variable $$X$$ has $$Var(X) = 2$$ and $$E(X) = 3. $$What is the standard deviation $$SD(X)$$?

Accepted Answer

$$\sqrt{2}$$

Question 14

Which formula gives the probability of $$r$$ successes in $$n$$ binomial trials with probability $$p of $$success?

Accepted Answer

$$P(X=r) = \binom{n}{r} p^r (1-p$$)^{n-r}$$

Question 15

A fire insurance policy pays out $$200,000$$ with probability $$\frac{1}{10,000}$$ and $$0$$ otherwise. What is the expected payout?

Accepted Answer

$$20$$

Question 16

Which of the following is NOT a requirement for using the Poisson distribution?

Accepted Answer

There must be a fixed number of trials.

Question 17

If $$X is a $$discrete random variable with $$E(X^2) = 10$ and E(X) = 2$, what is $$Var(X)$$?

Accepted Answer

$$6$$

Question 18

A box contains 20 tax return forms. $$X is $$the number of forms with an error. Which type of random variable is $$X$$?

Accepted Answer

Discrete

Question 19

Which of the following is the correct formula for the probability of $$r$$ events in a Poisson distribution with mean $$\lambda$$?

Accepted Answer

$$P(X=r) = \frac{e$$^{-\lambda}$$ \lambda^r}{r!}$$

Question 20

A random variable $$X is $$defined as the number of sales in 10 cold calls. Which distribution is most appropriate to model $$X$$?

Accepted Answer

Binomial

L7 Discrete Random Variables and Probability Distributions: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드