Q3: Statistics and Probability Exam

1. It is a function that associates a real number to each element in the sample space.

• Continuous

• Discrete

• Random Variable

• Sample Space

2. Which of the following random variable is continuous?

• Test score

• Amount of water in a jar

• Eggs in a tray

• Population of dogs

3. In tossing three coins, what are the possible values for the number of heads?

• 0, 1, 2, 3

• 1, 2, 3, 4

• 2, 3, 4, 5

• 3, 4, 5, 6

4. The probability distribution of a discrete random variable is called a probability mass function.

• True

• False

• Sometimes true

• Sometimes flase

5. Which of the following random variables would you expect to be discrete?

• The lifetime of capacitors

• The number of children at a Birthday Party

• The weights of mechanically produced goods

• The distance between Mount Bagarabon Resort of Mabua to El Solana Resort of Looc.

6. Let f(x) = k(x) for x = 0, 1, 2, 3. Solve for k so that f(x) satisfies the two properties of

being a probability mass function.

• k =1/4

• k =1/5

• k =1/6

• k =1/7

7. Which of the following statements is true about a probability distribution?

• A probability distribution is equal to one.

• A probability distribution shows the frequency distribution of a random variable.

• A continuous probability distribution is used to summarize a discrete random variable.

• A probability distribution summarizes all possible experimental outcomes and their probability.

Examine the relationship of standard deviation with variance through the formula:

sd^𝟐 = ∑ [(𝒙 − μ) ^𝟐 P(𝒙)].

• Variance is the cube root of standard deviation.

• Standard deviation is just a square of the variance.

• Variance is the square root of the standard deviation.

• Standard deviation is just a square root of the variance.

9. Which of the following is needed to find the expected value?

• Mean of the outcome

• Variance of the outcome

• Probability of the outcome

• Standard Deviation of the outcome

10. Adam and Eve bought a tray containing 6 eggs. The seller of the eggs informs them that, “the expected number of broken eggs per tray is 0.12.” What does the seller mean?

• The probability that one of these trays contains 6 broken eggs.

• For every 100 trays, we can predict about 12 broken eggs in total.

• For every 6 eggs, there is a zero probability that the egg is broken.

• The probability that one of these trays contains a broken egg is 0.12 on average.