Understanding Binomial Variables

This video tutorial explores the expected value and variance of binomial variables. It begins with an introduction to binomial variables, explaining their definition and properties. The tutorial then delves into calculating the expected value, using the properties of expected values and Bernoulli variables. Following this, the video explains how to determine the variance of binomial variables, including a detailed breakdown of the variance formula. Finally, an example is provided to illustrate the calculation of variance and standard deviation in a practical scenario.

What is a binomial variable X defined as?

• The sum of probabilities in n trials

• The number of successes in n trials

• The number of failures in n trials

• The probability of success in a single trial

How is the expected value of a binomial variable X calculated?

• As the sum of probabilities of all trials

• As the product of n and the expected value of a Bernoulli variable

• As the difference between successes and failures

• As the square of the probability of success

What is the expected value of a Bernoulli variable Y?

• 1 - p

• 0

• p

• n * p

Which property allows the calculation of variance for a binomial variable?

• Sum of standard deviations

• Difference of probabilities

• Product of expected values

• Sum of variances

What is the variance of a Bernoulli variable Y?

• p^2

• 1 - p

• n * p

• p(1 - p)

How is the variance of a binomial variable X expressed?

• n * p^2

• n * p * (1 - p)

• p * (1 - p)

• n^2 * p

In the example of free throws, what is the probability of success?

• 1.0

• 0.5

• 0.3

• 0.7

What is the variance of the number of successful free throws in the example?

• 3.0

• 2.1

• 1.5

• 0.9

How do you calculate the standard deviation from the variance?

• Divide the variance by n

• Take the square root of the variance

• Add the variance to p

• Multiply the variance by n

What is the standard deviation of the number of successful free throws in the example?

• 0.7

• 1.45

• 1.0

• 2.1