Question 1

Which of the following statements best describes a discrete random variable?

Accepted Answer

It can only take on a finite or countably infinite set of values.

Question 2

Given the probability distribution for the number of cars sold per day at a dealership: $$P(X=0)=0.18$$, $$P(X=1)=0.39$$, $$P(X=2)=0.24$$, $$P(X=3)=0.14$$, $$P(X=4)=0.04$$, $$P(X=5)=0.01$$, what is the probability that at most 2 cars are sold in a day?

Accepted Answer

$$0.81$$

Question 3

Which of the following is NOT a requirement for a valid probability mass function $$f(x)$$ for a discrete random variable?

Accepted Answer

All $$f(x)$$ must be equal for all $$x$$

Question 4

A random variable $$X$$ has the following probability mass function: $$f(x) = \frac{x}{10}$$ for $$x = 1, 2, 3, 4. $$What is $$P(X=3)$$?

Accepted Answer

$$0.3$$

Question 5

Suppose $$X is $$the number of dots facing up when rolling a fair six-sided die. What is the probability mass function $$f(x)$$ for $$X$$?

Accepted Answer

$$f(x) = \frac{1}{6}$$ for $$x = 1, 2, 3, 4, 5, 6$$

Question 6

Given the probability distribution for the number of cars sold per day, what is the expected value $$E(X)$$?

Accepted Answer

$$1.5$$

Question 7

For the same distribution, what is the variance $$Var(X)$$?

Accepted Answer

$$1.25$$

Question 8

A psychologist finds the number of hours to gain a patient's trust is $$X = 1, 2, 3$$ with $$f(x) = \frac{x}{6}. $$What is the probability that it takes at least 2 hours?

Accepted Answer

$$0.8333$$

Question 9

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

Accepted Answer

The probability of success changes from trial to trial.

Question 10

Let $$X \sim Bin(3, 0.3). $$What is $$P(X=2)$$?

Accepted Answer

$$0.189$$

Question 11

Suppose $$X \sim Bin(10, 0.3). $$What is the expected value $$E(X)$$?

Accepted Answer

$$3$$

Question 12

For $$X \sim Bin(10, 0.3)$$, what is the probability that at most 3 customers make a purchase?

Accepted Answer

$$0.6496$$

Question 13

For $$X \sim Bin(10, 0.3)$$, what is the probability that more than 2 but less than 5 customers make a purchase?

Accepted Answer

$$0.4669$$

Question 14

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

Accepted Answer

$$f(x) = \binom{n}{x} p^x (1-p$$)^{n-x}$$

Question 15

Which of the following is a property of a probability density function (pdf) for a continuous random variable?

Accepted Answer

$$f(x) \u003e 0$$ for all $$x$$

Question 16

For a continuous random variable $$X$$ with pdf $$f(x)$$, what is the probability that $$X$$ falls in the interval $$[a, b]$$?

Accepted Answer

$$P(a \leq X \leq b) = \int_a^b f(x) dx$$

Question 17

Which of the following best describes the difference between a probability mass function (pmf) and a probability density function (pdf)?

Accepted Answer

A pmf is used for discrete random variables, while a pdf is used for continuous random variables.

Question 18

If $$X is a $$continuous random variable, which of the following is always true?

Accepted Answer

$$P(X = x) = 0$$ for any specific value $$x$$

Discrete Probability Distributions: Concepts, Calculations, and the Binomial Distribution

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