Statistics - Theorem's & Rules

What 3 things are true about the data under Empirical Rule?

1 - Approx 68% of data values will fall w/in 1 standard deviations 2 - Approx 95% of data values will fall w/in 2 standard deviations 3 - Approx 99.7% of data values will fall w/in 3 standard deviations

According to Chebyshev's Theorem, at least what proportion of the data will be within μ ± kσ for k = 2?

75%

According to Chebyshev's Theorem, at least what proportion of the data will be within μ ± kσ for k = 3?

88.89%

Joint Events

An event that has two or more characteristics Example - Getting 2 heads when tossing a coin twice.

When the data distribution is bell shaped (or what is called normal) what rule can you use?

Empirical Rule

Complement

Of event A includes all events not part of A.

Multiplication Rule of Independent Events

P(A and B) = P(A)*P(B)

Addition Rule of Probability

P(A or B) = P(A) + P(B) - P(AB)

Multiplication Rule 2: Dependent Events

P(B/A) = P(AandB)/P(A) Means prob of B, given A has already happened. Also, P(A/B)=P(AandB)/P(B) Means prob of A given B has already happened

Chebyshev's Theorem applies to any distribution of data, regardless of shape? T or F

TRUE

For 2nd multiplication rule: dependent events, which event do you divide by

The event that has already happened

Chebyshev's Theorem

The proportion (or fraction) of any set of data lying within K standard deviations of the mean is always at least 1-1/K2, where K is any positive number greater than 1.

Mutually Exclusive Events

Two events that cannot occur at the same time

Sample Space

the collection of all possible outcomes/events