probability and statistical inference

Question 1

1. Outline statistical reasoning

Answer 1

Statistical reasoning is the way people reason with statistical ideas and make sense of statistical information.

Question 2

2. What is Bernoulli’s theorem?

Answer 2

Bernoulli’s theorem says that the relative frequency of success in a sequence of Bernoulli trials approaches the probability of success as the number of trials increases towards infinity.

Question 3

3. What is Chebyshev’s Law?

Answer 3

Chebyshev’s inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean.

Question 4

4. What is the law of averages?

Answer 4

The law of averages state that the supposed principle that future events are likely to turn out so that they balance any past deviation from a presumed average. However, there is No “Law of Averages.”

Question 5

5. What are independent and dependent events?

Answer 5

An independent event is an event that has no connection to another event’s chances of happening (or not happening). When two events are dependent events, one event influences the probability of another event. A dependent event is an event that relies on another event to happen first.

Question 6

6. What does dilution of the unlikely mean?

Answer 6

Dilution of large numbers works not by “balancing out” prior unlikely outcomes, but by diluting their effect on the average in the long term.

Question 7

7. What is a binomial distribution?

Answer 7

Binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

Question 8

8. What is margin for error?

Answer 8

A margin of error tells you how many percentage points your results will differ from the real population value.

Question 9

9. What is standard deviation and how to calculate it?

Answer 9

The Standard Deviation is a measure of how spread out numbers are. It is the square root of the variance which is the average of the squared differences from the mean.

Question 10

10. What are outliers?

Answer 10

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.