Download Midterm Review Sheet

Stat 160 Midterm Review
Chapter 1 – Descriptive Statistics
 Shapes of Distributions
o Symmetric, asymmetric, right skewed, left skewed, etc.
 Five Number Summary
o (Min,Q1,Med,Q3,Max)
o Boxplots
o Identifying outliers (LIF and UIF)
 Other Statistics
o Measures of Center
 Sample Median* - Q2
 Sample Mean* - x
 HL Estimate*
o Measures of Scale
 Range*
 IQR* = Q3 – Q1
 Sample Variance/Standard Deviaiton – s2/s
 Linear Relationships
o Prediction Equation - Yˆ  aˆ  bˆx
o Meaning of the intercept and the slope
o Residuals - eˆ  Y  Yˆ
o Correlation Coefficient – r
o Coefficient of Determination – R2
o Determination of a good model
 Robust Statistics
o Which of the statistics given above are robust?
Chapter 2 - Probability
 Tree Diagrams
 Sampling with replacement OR without replacement.
#A
 Relative Frequency - Pˆ ( A) 
N
 Independence
o P(B|A) = P(B) i.e. event B does NOT depend on event A.
 Useful Formulas
o In general, P(A and B) = P(B|A)P(A) = P(A|B)P(B)
o If A and B are independent, P(A and B) = P(A)P(B)
o Complement – P(AC) = 1 – P(A)
Chapter 3 – Resampling/Simulation
 Experiment
o Trials of the experiment are independent and taken under identical
conditions.
#A
Pˆ ( A) 
 pˆ , A-Event of Interest and N – Number of Trials
N
pˆ (1  pˆ )
o Error = 2
N
o Setting up the correct model (GA#7)
 (Number of Trials, Min Value, Max Value, Number Drawn, with
replacement or without replacement)
o
Chapter 4 – Probability Models for Discrete Distributions
 Probability Model
o Mean -   SumX  P(X ) for all values in the Range of X




o Variance -  2  Sum ( X   ) 2  P( X ) for all values in the Range of X
Binomial Distribution
o X is the # of Successes out of n trials with P(S) = p.
o X is Bin(n,p). Range of X is {0,1,2,…,n}
o Mean -   np
o Variance -  2  np(1  p)
o P ( X  k )  pbinom(k,n,p). P(of at most k successes)
o P(X = k) = dbinom(k,n,p). P(exactly k successes)
Poisson Distribution
o X is a count over some time interval. The average occurrence over that
interval is  .
o If 2 intervals do NOT overlap then the occurrence of events in these
intervals are independent.
o X is POI(  ). Range of X = {0,1,2,…}
o P ( X  k )  ppois(k,n,p). P(of at most k)
o P(X = k) = dpois(k,n,p). P(exactly k)
Chapter 5 – Probability Models for Continuous Distributions
 Uniform Distribution
 Normal Distribution
o Symmetric bell-shaped curve (i.e. median = mean)
o X is N(2) – Mean = Variance = 2
o P(X<k) = pnorm(k,). Note: 3rd input is standard deviation NOT
variance.
o P(X>k) = 1 - pnorm(k,).
o P(a<X<b) = pnorm(b,) - pnorm(a,).
Chapter 6 – Central Limit Thoerem
 If X is a random variable from some distribution with mean, and variance, 2,
2
then the sample mean ( x ) of a random sample of size, n, is N  , n .
 Apply Chapter 5 to solve probability problems based on the normality of x .

