Probability Distributions and Expected Value

Which one of the following is a discrete random variable?

• Sam's height

• Sam weight

• Time Sam's runs the 110 m hurdles

• Amount of Sam's brothers and sisters

Classify: How many miles it takes to use up a tank of gas.

• Discrete

• Continuous

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.

• Discrete
• Continuous

• Discrete
• Continuous

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?

• 0.20
• 0.29
• 0.39
• 0.61

The table represents the probability of guessing correct on a 5 question true-false quiz.  Find the probability for at least 4 questions correct.

• .03125
• .15625
• .3125
• .1875