Question 1

Which of the following is a requirement for a probability distribution?

Accepted Answer

The sum of all probabilities must equal 1.

Question 2

Given the probability distribution for the number of females in two births: $$x = 0, 1, 2$$ with $$P(x) = 0.25, 0.50, 0.25$$ respectively, what is the mean number of females?

Accepted Answer

$$\mu = 1.0$$

Question 3

Which formula correctly calculates the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum [(x - \mu)^2$ \cdot P(x)]$$

Question 4

A table lists countries and the proportion of unlicensed software in each. Why does this table NOT describe a probability distribution?

Accepted Answer

The values of x are not numerical and the probabilities do not sum to 1.

Question 5

If $$P(x) = \frac{1}{2(2-x)!x!}$$ for $$x = 0, 1, 2$$, what is $$P(1)$$?

Accepted Answer

$$0.50$$

Question 6

Which of the following best describes a discrete random variable?

Accepted Answer

A variable with a finite or countably infinite set of values.

Question 7

What is the expected value $$E$$ for a discrete random variable $$x$$ with probability distribution $$P(x)$$?

Accepted Answer

$$E = \sum [x \cdot P(x)]$$

Question 8

A probability histogram differs from a relative frequency histogram in that:

Accepted Answer

It uses probabilities on the vertical axis instead of relative frequencies.

Question 9

If the variance of a probability distribution is $$0.5$$, what is the standard deviation?

Accepted Answer

$$0.7$$

Question 10

Which of the following is TRUE about the parameters of a probability distribution?

Accepted Answer

They describe the entire population.

Question 11

Suppose you bet $$5 on the number 7 in roulette. The probability of losing 5 is$$ $$\frac{37}{38}$$ and the probability of winning $$175 is $$\frac{1}{38}$. What is the expected value of your bet?

Accepted Answer

$$-0.26$$

Question 12

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

The sum of all probabilities must be less than 1.

Question 13

If a value is considered 'significantly low' in a probability distribution, which of the following is true?

Accepted Answer

It is at most $$\mu - 2\sigma.$$

Question 14

A probability distribution has $$P(x) = 0.2, 0.5, 0.3$$ for $$x = 1, 2, 3. $$What is the mean $$\mu$$?

Accepted Answer

$$\mu = 2.1$$

Question 15

Which scenario best illustrates a continuous random variable?

Accepted Answer

The height of students in a classroom.

Question 16

If the probability of an event is negative, what does this indicate?

Accepted Answer

There is an error, as probabilities cannot be negative.

Question 17

Which of the following is the correct formula for the standard deviation $$\sigma of a $$discrete probability distribution?

Accepted Answer

$$\sigma = \sqrt{\sum [x^2$ \cdot P(x)] - \mu^2$}$$

Question 18

If you bet $$5 on the pass line in craps, with a probability of losing 5$ being $$\frac{251}{495}$$ and winning 5$ being $$\frac{244}{495}$, what is your expected value?

Accepted Answer

$$-0.07$$

Question 19

Which bet is better in the long run based on expected value: betting $$5 on the number 7 in roulette or 5 on $$the pass line in craps?

Accepted Answer

Craps, because the expected loss is smaller.

Probability Distributions: Concepts, Calculations, and Applications

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