Question 1

Which of the following best describes the distribution of 'Month of Birth' in a large, randomly selected population?

Accepted Answer

Uniform distribution

Question 2

Suppose you are analyzing the number of West Nile Virus (WNV) cases reported in each county in a given year. Which probability distribution is most appropriate for modeling the number of cases per county?

Accepted Answer

Poisson distribution

Question 3

If the probability of being diagnosed with WNV is independent of age group, what is the expected number of cases in each age group proportional to?

Accepted Answer

The frequency of the age group in the population

Question 4

Which of the following is a key property of a probability distribution for a discrete random variable?

Accepted Answer

The sum of all probabilities must equal 1

Question 5

A researcher records the number of siblings for each student in a class. Which distribution is most appropriate for modeling this data?

Accepted Answer

Poisson distribution

Question 6

Given two independent events $$A$$ and $$B$$, what is the probability that both $$A$$ and $$B$$ occur?

Accepted Answer

$$P(A) 	imes P(B)$$

Question 7

If the probability of an event $$A is$$ $$0.3$$, what is the probability of the complement event $$A^c$$?

Accepted Answer

$$0.7$$

Question 8

Which of the following is an example of a continuous random variable?

Accepted Answer

Concentration of a chemical in blood

Question 9

A die is rolled once. Let $$A be $$the event 'rolling a 1' and $$B be $$the event 'rolling a 5'. What is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$\frac{2}{6}$$

Question 10

Which distribution is most appropriate for modeling the latency (time until) of infection in a biological process, where the variable is continuous and strictly positive?

Accepted Answer

Log-normal distribution

Question 11

If the probability of being diagnosed with WNV is not independent of age group, which statistical concept is violated?

Accepted Answer

Independence

Question 12

Suppose the probability of a randomly selected person being in age group 65-100 is $$0.086$$, and the probability of dying from WNV given that a person is in this age group is $$0.096. $$What is the joint probability that a randomly selected person is in age group 65-100 and dies from WNV?

Accepted Answer

$$0.086 	imes 0.096$$

Question 13

Which of the following best describes a multinomial distribution?

Accepted Answer

A distribution where each trial results in one of $$k$$ categories, with fixed probabilities for each category

Question 14

A random variable $$X$$ has a continuous uniform distribution on the interval $$[a, b]. $$What is the probability that $$X$$ falls between $$c$$ and $$d$$, where $$a \leq c \u003c d \leq b$$?

Accepted Answer

$$\frac{d-c}{b-a}$$

Question 15

In a study, the observed number of WNV cases in the 45-64 age group is much higher than expected based on census data. What does this suggest?

Accepted Answer

The 45-64 age group is more likely to be diagnosed with WNV

Question 16

Which of the following is a correct statement about mutually exclusive events?

Accepted Answer

The probability of both occurring is zero

Question 17

A patient died of WNV. What is the probability that the patient was a senior (65 or older), given that 19 out of 26 deaths were in this age group?

Accepted Answer

$$\frac{19}{26}$$

Question 18

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

Accepted Answer

Probabilities can be negative for rare events

Question 19

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 20

Which distribution is most appropriate for modeling the age at which individuals are diagnosed with a disease, assuming the data are continuous and right-skewed?

Accepted Answer

Weibull distribution

Null Models and Probability Distributions in Biological Data

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