Understanding Geometric Random Variables

The video tutorial explains a game involving rolling a die until a one appears, defining a random variable X as the number of rolls needed. It calculates probabilities for different values of X, introduces geometric random variables, and discusses their mean and standard deviation. The tutorial also covers the distribution characteristics of geometric variables, highlighting their right-skewed nature. Finally, it explores a scenario using a 12-sided die, comparing the mean and standard deviation to the original six-sided die scenario.

What is the random variable X defined as in the game?

• The number of times a 6 is rolled

• The number of times a 1 is rolled

• The number of rolls until a 1 is obtained

• The total number of rolls in the game

What is the probability that X equals 2?

• 5/6

• 1/36

• 5/36

• 1/6

What type of random variable is X?

• Binomial

• Geometric

• Poisson

• Normal

How is the mean of a geometric random variable calculated?

• Number of trials divided by the probability of success

• Probability of failure divided by the probability of success

• 1 divided by the probability of success

• Probability of success times the number of trials

What is the mean number of rolls to get a 1 with a six-sided die?

• 12

• 6

• 1

• 3

How is the standard deviation of a geometric random variable calculated?

• Probability of success times the mean

• Square root of probability of success

• Mean divided by the probability of success

• Mean times the square root of 1 minus probability of success

What is the approximate standard deviation for a six-sided die?

• 4.5

• 5.5

• 7

• 6

What is a characteristic of the distribution of a geometric random variable?

• Left skewed

• Symmetrical

• Uniform

• Right skewed

What would be the mean number of rolls to get a 1 with a twelve-sided die?

• 18

• 24

• 6

• 12

What is the approximate standard deviation for a twelve-sided die?

• 10.5

• 11.5

• 12.5

• 13.5