Probability and Statistics Concepts

What is the focus of the third day of probability lessons?

• Sampling distributions

• Geometric distributions

• Conditional probability

• Random variables

Which of the following is a characteristic of a discrete random variable?

• The sum of its probabilities is less than one

• It can take an infinite number of values

• It is always normally distributed

• It can only take a countable number of values

In a binomial setting, what is required for the trials?

• They must be dependent

• They must be independent

• They must have varying probabilities of success

• They must be infinite

Why can't standard deviations be added directly?

• Because they are not independent

• Because they are not variances

• Because they are not means

• Because they are always zero

What is the expected value of a random variable?

• The average of all possible outcomes

• The most frequent outcome

• The sum of all possible outcomes

• The probability of the most likely outcome

What is the main advantage of Machine B in the photocopier problem?

• Lower initial cost

• Unlimited repairs

• Lower expected total cost

• Higher reliability

What is the probability that all three ATMs are working given that at least one is working?

• 0.28

• 0.24

• 0.15

• 0.40

What is the significance of the sentence 'students who do well on the verbal portion of the SAT tend to do well on the mathematics portion'?

• It implies the events are conditional

• It shows the events are mutually exclusive

• It suggests the events are dependent

• It indicates the events are independent

What should be done if a student does not have access to the internet for the exam?

• Skip the exam

• Wait for the next exam

• Contact the College Board

• Use a friend's device

What is the expected value of the number of ATMs working when the mall opens?

• 1.73

• 1.00

• 2.00

• 2.50