Quiz

Question 1

What are the permutations of n different elements taken n at a time and what is their number?

Answer 1

Permutations are all the possible linear arrangements of all the elements.

Question 2

Define the combinations of n different elements taken k at a time in words.

Answer 2

All possible selections of size k of different elements.

Question 3

What is the meaning of the (n / k) binomial coefficient? Define it with a formula and with reference to combinatorics.

Answer 3

The binomial coefficient gives the number of ways k elements can be chosen from n different elements without regard to order.

Question 4

Describe the relationship between the probabilities of event A and its complement event B.

Answer 4

P(A) + P(B) = 1

Question 5

Define the sum of events A and B.

Answer 5

Sum of A and B is the event which occurs when either A or B or both occur.

Question 6

What is the probability of the sum of events A and B?

Answer 6

P(A + B) = P(A) + P(B) - P(AB)

where (A + B) is the sum of events A and B.
and (AB) is the products of events A and B.

Question 7

Define the product of events A and B.

Answer 7

Product of A and B is the event which occurs when both A and B occur.

Question 8

Define the complement event of event A.

Answer 8

Is the event which occurs when A doesn’t occur and the sum of the probabilities of A and its complement event is 1.

Question 9

When are events A and B exclusive?

Answer 9

It is when AB = 0.

Question 10

When are events A and B independent of each other?

Answer 10

Only if event B has no effect on the probability of event A and vice versa.

Question 11

Using the terms of set theory define:
a. the product of events A and B.
b. the sum of events A and B.

Answer 11

a. AB — the intersection of events A and B.
b. A + B — the union of events A and B.

Question 12

What is the meaning of P(A|B)?

Answer 12

It is a conditional probability of A given B. And the probability of A occurring is dependent on B.

Question 13

What is the definition of a random variable?

Answer 13

Is the number assigned to a random event.

Question 14

What is a continuous random variable?

Answer 14

A random variable is continuous if it can assume any value within a specified interval of values.

Question 15

What is the definition of the cumulative relative frequency of a sample?

Answer 15

Cumulative relative frequency of a sample at x gives the fraction of elements in the sample which are smaller than or equal to x.

Question 16

Define the mean of a discrete random variable.

Answer 16

xi — is the ith value of the random variable.
pi — is the probability that the random variable assumes the value of xi.

Question 17

Define the variance of a random variable.

Answer 17

Is the squared deviation of a random variable from its mean.

Question 18

Define the variance of a sample in words.

Answer 18

A statistic estimating the variance of a random variable or population from which the sample has been taken.

Question 19

Define the standard deviation (SD) and the standard error of the mean (SEM) of a sample with formulas.

Answer 19

xi — the sample of elements.
x̄ — is the mean of the sample.
n — is the number of elements in the sample.

Question 20

Define the coefficient of variation (CV) in words, and with a formula.

Answer 20

Coefficient of Variation (CV) is the standard deviation (SD) expressed as the percentage of the mean (x̄):

CV = (SD / x̄) * 100

Question 21

What is an ordered array?

Answer 21

Is a listing of the values of a sample from the smallest to the largest values.

Question 22

Define the i-th percentile of a sample.

Answer 22

Is the smallest sample value that is equal to or greater than i% of the observations.

Question 23

Define the first, second and third quartile (Q1, Q2, Q3) of a sample.

Answer 23

Q1 is the 25th percentile, Q2 is the 50th percentile (or the median), Q3 is the 75th percentile.

Question 24

Define the mode of a sample.

Answer 24

Is the value which occurs the most frequently.

Question 25

Give the kth element of a binomial distribution with parameter p (the probability of the first possible outcome of a trial) if the total number of trials n (k = 0, 1, 2, 3…, n), and define the probability it means.

Answer 25

Pn,k is the probability that a given event occurs k times in n independent trials with two possible outcomes with probabilities p and 1-p:

Question 26

Give the sum of the elements of a Poisson distribution with parameter λ.

Answer 26

Question 27

What is a type I error in a statistical test?

Answer 27

True hypothesis (✓) — ACCEPTED
Null hypothesis (✗) — REJECTED

Question 28

What is a type II error in a statistical test?

Answer 28

True hypothesis (✗) — REJECTED
Null hypothesis (✓) — ACCEPTED

Question 29

When is a sample representative?

Answer 29

When we use random sampling (i.e. each element of the population has equal probability of being sampled)

Question 30

What are the most important attributes of the quality of an estimates? Define them briefly.

Answer 30

1. Accuracy or unbiasedness — Value equal to the mean of the estimated parameter.

2. Precision or reproducibility — Value of the SD is small.

Question 31

Write the null hypothesis for an F test

Answer 31

Variances of the two populations under investigation are equal.

Question 32

What is the definition of specificity of a clinical diagnostic test?

Answer 32

Specificity is the probability of obtaining a negative test result in a patient without the examined diseases condition (i.e. the reliability of the test in correctly identifying those patients who do not have the condition)

P(T- | D-)

Question 33

What is the definition of sensitivity of a clinical diagnostic test?

Answer 33

Sensitivity is the probability of obtaining a positive test result in a patient who has the examined diseases condition (i.e. the reliability of the test in correctly detecting those patients who have the condition)

P(T+ | D+)

Question 34

What is the definition of negative predictive value?

Answer 34

Negative predictive value is the probability that a subject with a negative test result does not have the disease condition.

P(D- | T-)

Question 35

Give the kth element of a Poisson distribution with parameter λ and define the probability it means.

Answer 35

Pk — is the probability that the given event occurs k number of times in an infinite number of independent trials.

Question 36

What is the definition of the cumulative distribution function of a random variable?

Answer 36

Cumulative distribution function (CDF) of a random variable at x gives the probability that the random variable assumes a value smaller than or equal to x

Question 37

What is the probability that a continuous random variable assumes a value in the interval between a and b?

Answer 37

The probability is equal to the area under the curve of the probability density function between a and b