Random Variables

Word Cloud

What is statistics?

Word Cloud

What is probability?

Multiple Select

Which of the following are characteristics of descriptive statistics?

• Compiling and summarizing data

• Drawing conclusions about a population

• Displaying data using tables and charts

• Using sample data to infer about a population

Multiple Choice

Which of the following best describes probabilistic reasoning?

• Predicting the sample based on known population proportions

• Estimating the population from a random sample

• Selecting a random sample from the population

• Calculating the mean of a sample

Multiple Select

Which of the following statements about random variables are correct?

• They assume values as a result of random events

• They are denoted by capital letters

• They always represent the entire population

• They can take several different values

Multiple Choice

As the sample size increases, the relative frequency tends to approach which of the following?

• The mean

• The probability

• The median

• The mode

Multiple Choice

Which of the following is an example of an experiment in probability?

• The probability of drawing a yellow candy

• Tossing a coin twice

• The complement of an event

• The union of two events

Multiple Choice

Which of the following best describes an event in probability?

• The set of all possible outcomes of a statistical experiment

• A subset of the sample space

• A description of some chance process

• The probability for each outcome

Multiple Choice

If two events A and B are mutually exclusive, what is true?

• A and B can happen simultaneously

• A and B have no elements in common

• A and B are always independent

• A and B always sum to 1

Multiple Choice

What is a sample space in probability?

• The probability of an event occurring

• The average value of an experiment

• The complement of an event

• A set of all possible outcomes of an experiment

Multiple Choice

If an event A can never occur, what is the value of P(A)?

• 1

• 0

• 0.5

• Cannot be determined

Multiple Choice

Which of the following is a common method for finding probabilities?

• Estimates from empirical studies

• Guessing based on intuition

• Using only past experiences

• Ignoring equally likely events

Multiple Select

Which of the following are possible outcomes when throwing a pair of dice?

• (1,1)

• (2,3)

• (6,6)

• (7,2)

Multiple Choice

What is the probability that the sum of the numbers on two dice is 6?

• 2/36

• 5/36

• 6/36

• 1/6

Multiple Choice

What is the probability of getting fewer than 3 heads when tossing a fair coin 3 times?

• 1/8

• 3/8

• 7/8

• 1/8

Multiple Choice

If a fair coin is tossed three times, what is the probability of getting at least two heads?

• 1/8

• 3/8

• 2/8

• 1/2

Multiple Choice

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

Multiple Choice

A discrete random variable is one that:

• Can take any value within a given range.

• Takes a fixed set of possible values with gaps between.

• Has a probability density function.

• Represents continuous measurements like height or weight.

Multiple Choice

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

• The number of students passing an exam

• The weight of a newborn baby

• The amount of rainfall in a city

• The waiting time for a bus

Multiple Choice

Which of the following statements about continuous random variables is true?

• They have a countable number of possible values

• Their probability distribution is represented by a probability mass function

• They can take an infinite number of values within an interval

• They are always greater than 1

Multiple Choice

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

• The number of cars sold daily.

• The score on a personality test (1 to 5).

• The height of a person.

• The number of heads obtained in coin tosses.

Multiple Choice

Which of the following is a valid discrete probability distribution?

• P(X=1) = 0.2, P(X=2) = 0.3, P(X=3) = 0.5

• P(X=1) = 0.2, P(X=2) = 0.3, P(X=3) = 0.6

• P(X=1) = 0.2, P(X=2) = 0.3, P(X=3) = 0.4

• P(X=1) = 0.2, P(X=2) = 0.3, P(X=3) = 0.2

Multiple Choice

What is the probability of drawing a value of 4 from the probability distribution below?

• 0.28

• 0.16

• 0.2

• 0.14

Multiple Choice

What is the probability of selling more than 2 cars per day if the probability distribution is given as:

• 0.25

• 0.35

• 0.45

• 0.55

Multiple Choice

The cumulative distribution function (CDF) for a random variable X is defined as:

• P(X = x)

• The sum of all probabilities

• P(X ≤ x)

• The mean of X

Multiple Choice

What is the cumulative distribution function (CDF) of a discrete random variable X?

• The probability that X is less than or equal to a certain value

• The probability that X is greater than a certain value

• The probability that X is equal to a certain value

• The probability that X is not equal to a certain value

Multiple Choice

The expected value (mean) of a probability distribution is calculated as:

• The highest probability value in the distribution

• The sum of all probabilities divided by the number of outcomes

• The sum of each outcome multiplied by its probability

• The product of the largest and smallest probability value

Multiple Choice

A psychologist administered a personality test and assigned scores from 1 to 5. The probability distribution is given below:
what is the mean score?

• 2

• 2.5

• 2.94

• 3

Multiple Choice

A psychologist administered a personality test and assigned scores from 1 to 5. The probability distribution is given below:
what is the variance?

• 1.616

• 2.5

• 2.94

• 3

Multiple Choice

It is known that E[X] = 2 for a given random variable X and var(X) = 5. Determine E[X²].

• 1

• 3

• 4

• 7

• 9

Multiple Choice

Which of the following statements about continuous random variables is true?

• They have a countable number of possible values

• Their probability distribution is represented by a probability mass function

• They can take an infinite number of values within an interval

• They are always greater than 1

Categorize

Options (16)

Number of students in class who scored A for Algorithm

The weight of students in FSKTM

Number of road accidents in year 2000-2009

Number of goals scored in a soccer match

Number of cars in a parking lot

Number of students who passed an exam

Number of pets owned by families in a neighborhood

Number of times a coin lands on heads in 100 flips

Number of customers visiting a store in a day

The height of students in FSKTM

The temperature in a city over a week

The time taken to run a marathon

The distance traveled by a car in a day

The amount of rainfall in a month

The speed of a runner during a race

The volume of water in a reservoir

Organize these options into the right categories

Discrete Random Variable

Continuous Random Variable

Multiple Choice

Which of the following topics is NOT covered in Chapter 1 of Engineering Statistics?

• Probability density function (PDF)

• Hypothesis testing

• Cumulative distribution function (CDF)

• Mean, variance and standard variation

Multiple Choice

Which of the following best describes the significance of studying random variables in engineering statistics?

• They help in predicting outcomes in uncertain situations.

• They are only used for theoretical mathematics.

• They are not relevant to real-world engineering problems.

• They are used to avoid all types of errors in experiments.