Discrete Probability Distribution Quiz: Random Variable and Numerical Observations

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Questions and Answers

Which of the following is the definition of the mean value of a variable?

The most common value over a finite number of observations of the variable.

The mean value over an infinite number of observations of the variable. (correct)

The value that has the highest probability of occurring.

What is the first step in finding the variance of a discrete probability distribution?

Multiply the square of the difference of X and the mean by each value of the random variable.

Find the mean of the probability distribution. (correct)

Calculate the standard deviation.

Subtract the mean from each value of the random variable X.

Which statement is NOT true about the variance of a discrete random variable?

Variance is the average squared deviation from the mean.

Variance is always nonnegative.

Variance is a measure of the spread of the distribution.

Variance is always less than or equal to the mean. (correct)

What is the mean and variance of the probability distribution given in the text?

Mean = 1.66, Variance = 2.20 Signup and view all the answers

What would be the best interpretation of the mean of the probability distribution given in the text?

If we look at a large number of customers, then each customer, on the average, will have purchased about 1.66 tickets. Signup and view all the answers

Which probability value would satisfy the given probability distribution?

0.17 Signup and view all the answers

What term refers to a variable being measured to produce numerical observations associated with the random outcomes of a chance experiment?

Random variable Signup and view all the answers

Which of the following represents a discrete random variable?

The number of patients in a hospital Signup and view all the answers

What are the possible values of a random variable when a coin is tossed once?

Tail (T) and Head (H) Signup and view all the answers

Which of the following represents a discrete probability distribution?

X 1 2 3 4 P(X) 1/5 3/10 1/5 3/10 Signup and view all the answers

A fair coin is tossed three times. What is the probability that no heads will appear?

1/8 Signup and view all the answers

What does the expected value of a random variable represent?

The sum of each outcome multiplied by its probability Signup and view all the answers

What is the primary purpose of variance in a discrete probability distribution?

To measure how spread out the data points are from the mean Signup and view all the answers

If a discrete probability distribution has a high variance, what can be inferred about the data points?

They are widely spread out from the mean Signup and view all the answers

In the given scenario, if the club hosts the basketball game and it does not rain, what is the expected value?

$15,000 Signup and view all the answers

Based on the weather forecast, what is the probability of the club losing all the invested money?

0.2 or 20% Signup and view all the answers

Which property of the normal curve is incorrectly stated in the given information?

It is divided into positive 2 and negative 2 standard deviations Signup and view all the answers

If a student scores 78 on both the Math and English exams, which exam would have a higher standing for that score?

Math, because the mean is lower Signup and view all the answers

Study Notes

Statistics and Probability

A random variable is a variable being measured to produce numerical observations associated with the random outcomes of a chance experiment.

Types of Random Variables

A discrete random variable is a variable that can only take on specific, distinct values (e.g., the number of patients in a hospital).
A discrete probability distribution is a table or formula that defines the probability of each value a discrete random variable can take.

Probability Distributions

A probability distribution lists all possible values of a random variable and their corresponding probabilities.
The sum of the probabilities in a probability distribution is equal to 1.

Coin Toss Probability

When a fair coin is tossed three times, the probability that no heads will appear is 1/8.

Expected Value

The expected value of a random variable is the mean value over an infinite number of observations of the variable.
It represents the average or "long-run" value of the variable.

Probability Distribution Properties

The variance of a probability distribution measures how spread out the data points are around the mean.
The variance is always non-negative.
High variance indicates that the data points are very spread out around the mean.

Calculating Variance

The first step in finding the variance of a discrete probability distribution is to calculate the mean of the probability distribution.

Normal Curve

A normal curve is a symmetrical, bell-shaped curve.
The total area under a normal curve is 1.
The mean, median, and mode have the same value and are located at the same point on a normal curve.
The area under the part of a normal curve in the standard normal distribution that lies within 2 standard deviations of the mean is approximately 95%.

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Description

Test your knowledge on probability distributions of random variables with this quiz. Includes questions on finding probability values from a given distribution. For example, determining the probability distribution of the number of tickets sold to a random customer.

Probability Distribution of Random Variable Quiz