Statistics 101 Discrete and Continuous Random Variables

Statistics 101

Discrete and Continuous Random Variables

Discrete Random Variable

Has a countable number of possible values

Getting Good Grades

An instructor of a large college course gives 15% of each A’s and D’s, 30% each B’s and C’s and 10% F’s. Student’s are grades on a four-point scale (A = 4).

Distribution of X:

Grade 0 1 2 3 4

Probability 0.10 0.15 0.30 0.30 0.15

Question

What is the probability that the student earned a B or better?

Is this the sum of an A and a B?

Answer

P(grade is 3 or 4)= P(3) + P(4) = 0.30 + 0.15 = 0.45

Probability histograms for (a) random digits and (b) Benford’s law

Example 7.2

Tossing Coins Assumptions

Balanced coin (Eric) Coin has no memory

X is the number of heads

Questions

P(X=2) = (number of ways X=2)/16 = 6/16

P(X=0) P(X=1) P(X=3) P(X=4)

P(X=0) = 1/16 = 0.0625 P(X=1) = 4/16 = 0.25 P(X=3) = 4/16 = 0.25 P(X=4) = 1/16 = 0.0625

Continuous random variables

Takes all values in an interval of numbers

Probability distribution – Described by a density curve

Random numbers and the uniform distribution (Ex:7.3 pg. 398)

Example 7.4 Drugs in Schools

1500 American Adults SRS N(0.3, 0.0118) What is the probability that the poll

differs from the truth about the population by more than two percentage points?

Z-score

XZ

Read Example p 401

Exercises 2, 4, 6, 8, 10, 15, 16, 19