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: Grade01234 Probability

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)  =  = 0.45

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 =  P(X=1) = 4/16 = 0.25  P(X=3) = 4/16 = 0.25  P(X=4) = 1/16 =

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, )  What is the probability that the poll differs from the truth about the population by more than two percentage points?

Z-score

Read Example p 401  Exercises 2, 4, 6, 8, 10, 15, 16, 19