5.2 - Probability Distributions & Expected Value

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

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

A stockbroker estimates that at the end of the year, there is a 40% chance a stock will be worth $50, a 35% chance it will be worth $60 and a 25% chance it will be worth $70.
What expected value does this broker assign to this stock's end-of-the-year price?

• $58.50
• $60.00
• $62.50
• $65.00

Probability can only be values between which two numbers?

• 0 to 2
• 0 to 10
• 0 to 5
• 0 to 1

Choose an American household at random. What is the expected number of cars for that household?

• 1.75
• 1.84
• 2.00
• 2.50

A random variable X has the following probability distribution: P(X=0) = 0.2, P(X=1) = 0.3, P(X=2) = 0.5. What is the expected value of X?

• 1.3

• 1

• 1.5

• 2

Suppose that 𝑥 represents the number of cars sold at a dealership in a randomly selected single day. The probability distribution of 𝑥 is given in the table.
What is the expected value of cars, 𝜇𝑥, sold per day at the dealership?

Discrete or Contiuous? Can there be a fraction of a car? Round up if discrete.