Question 1

Which of the following is a (are) required condition(s) for the distribution of a discrete random variable that can assume values  ?
A)
B)
C) Both (a) and (b) are required conditions.
D) The population data of the distribution must be quantitative.

Accepted Answer

The answer of Which of the following is a (are)...

Question 2

The probability of an event A is equal to the sum of the probabilities of the simple events contained in A.

Accepted Answer

This is one of the fundamental axioms of probability theory, also known as the "additive rule". It states that if we have a set of mutually exclusive and exhaustive events, the probability of any one of them occurring is equal to the sum of their individual probabilities.

Question 3

Relative frequency histograms are constructed for a sample of n measurements drawn from the population, whereas the probability histogram is constructed as a model for the entire population of measurements.

Accepted Answer

Relative frequency histograms represent the distribution of a sample, while probability histograms model the theoretical distribution of the entire population.

Question 4

Which of the following correctly describes the nature of discrete quantitative variables?

Accepted Answer

Discrete quantitative variables can only assume specific values with gaps between them, and the number of possible observations is finite, which aligns with both options (a) and (b).

Question 5

The probability distribution of the number of accidents in North York, Ontario, each day is given by  Which of the following could be used to describe this distribution?

Accepted Answer

The probability distribution is given by a probability mass function, which assigns probabilities to discrete values, indicating that it is a discrete probability distribution.

Question 6

In the case of independent events A, B, and C, which of the following is equal to  ?

Accepted Answer

The given expression 11eab386_b974_077e_aec0_a38845d70e8f_TB4962_11 is in fact the product of the probabilities of events A, B, and C. Therefore, the best choice is C, which is the product of P(A), P(B), and P(C).

Question 7

Which of these statements is a property of the probability distribution for a discrete random variable x ?

Accepted Answer

Option A is true because probabilities cannot be negative. Option B is also true because the sum of all the probabilities in the probability distribution of a discrete random variable x must be equal to one. Option C is false because the random variable x can take on any discrete value, not necessarily between 0 and 1. Therefore, the best choice is D, which includes both A and B as true.

Question 8

Probability is the tool that allows the statistician to use sample information to make inferences about or describe the population from which the sample was drawn.

Accepted Answer

This is a correct statement about the role of probability in statistics. Probability is essential for making accurate predictions or generalizations about a larger group based on a smaller sample. Without probability, it would be difficult to determine how likely it is that certain outcomes or patterns are representative of the larger population.

Question 9

A false negative in screening tests (e.g., steroid testing of athletes) represents which of the following events?

Accepted Answer

A false negative in screening tests means that the test result is negative even though the person actually has the condition being tested for. Therefore, option C is the correct answer. Options A and D refer to true negative and true positive results, respectively. Option B refers to a false positive result.

Question 10

Which of the following clearly describes the general multiplicative rule of probability?

Accepted Answer

The answer of Which of the following clearly describes the...

Question 11

A false positive in screening (e.g., home pregnancy tests) may be best described by which of the following events?

Accepted Answer

A false positive occurs when the test result is positive for a condition, but the person does not actually have the condition.

Question 12

What would be the expected number of heads turning up in 500 tosses of an unbiased coin?

Accepted Answer

An unbiased coin has a 50% chance of landing heads on each toss. Therefore, in 500 tosses, the expected number of heads is 0.5 * 500 = 250.

Question 13

Screening tests (e.g., HIV testing) are evaluated on the probability of a false negative or a false positive. How may one classify these probabilities?

Accepted Answer

False negative and false positive probabilities are both conditional probabilities because they measure the probability of a positive or negative result given the true state of the person being tested (i.e., whether they have the disease or not).

Question 14

Two events, A and B, are said to be dependent if and only if what condition is true?

Accepted Answer

Two events are dependent if the occurrence of event B affects or changes the probability of event A. In other words, the probability of A is dependent on the occurrence of B.

Question 15

The probability distribution of the number of accidents in North York, Ontario, each day is given in the table below:  Based on this distribution, what is the approximate value of the standard deviation of the number of accidents per day?

Accepted Answer

The answer of The probability distribution of the number of...

Question 16

What may NOT be said about the mean of a discrete random variable x?

Accepted Answer

The mean of a discrete random variable x is not necessarily the middle value of its probability distribution. The middle value is the median, not the mean.

Question 17

The probability distribution of the number of accidents in North York, Ontario, each day is given by  Based on this distribution, what would be the expected number of accidents on a given day?

Accepted Answer

The answer of The probability distribution of the number of...

Question 18

Statistics provides ways to reason from the population to the sample, whereas probability acts in reverse, moving from the sample to the population.

Accepted Answer

The statement is incorrect. Statistics deals with analyzing data from a sample to make inferences about the population, while probability analyzes the likelihood of an event occurring in the population based on the sample data.

Question 19

What is the term for a table, formula, or graph showing all possible values that a random variable x can assume, together with their associated probabilities p(x)?

Accepted Answer

This is the definition of a discrete probability distribution.

Question 20

Which of the following best describes the concept of marginal probability?

Accepted Answer

Marginal probability refers to the probability of a single event occurring without consideration of any other events.

Quiz 4: A: probability and Probability Distributions

Which of the following is a (are) required condition(s) for the distribution of a discrete random variable that can assume values ? A) B) C) Both (a) and (b) are required conditions. D) The population data of the distribution must be quantitative.