Discrete Distributions

A random variable is

• a hypothetical list of the possible outcomes of a random phenomenon.
• any phenomenon in which outcomes are equally likely.
• any number that changes in a predictable way in the long run.
• a variable whose value is a numerical outcome associated with a random phenomenon.

Which of the following is not a random variable?

• The heights of randomly-selected buildings in New York City.
• The suit of a card randomly-selected from a 52-card deck.
• The number of children in randomly-selected households in the United States.
• The amount of money won (or lost) by the next person to walk out of a casino in Las Vegas.

The number of runs scored by the Kansas City Royals in the last game of the World Series.

• Discrete

• Continuous

The amount of snow that falls in Brooklyn each February.

• Discrete

• Continuous

The weight of a newborn infant.

• Discrete

• Continuous

Which of the following is discrete data?

• Sammy is 160 cm tall.

• Sammy ran 100 m in 10.2 sec.

• Sammy weighs 60 kg.

• Sammy has 2 brothers and 1 sister.

Which of the following is NOT discrete data?

• The average life span of a human in the US is 79 years.

• A woman in the US has 2 children on average.

• The possible outcomes from rolling a die.

• Classes at BPCS have between 20 and 30 students.

Find the value of p.

• p = 0.11

• p = 0.21

• p = –0.89

What is the expected value of the random discrete value X?

• E(X) = 84.4

• E(X) = 85

• E(X) = 1

The table represents the probability of randomly guessing correctly on a 5 question true-false quiz. What is the expected value of correct answers on the quiz?

• E(X) = 1

• E(X) = 2.5

• E(X) = 3.91