Download FORMULA SHEET FOR MDM 4U1 EXAM

FORMULA SHEET FOR MDM 4U1 EXAM
ODDS
In favour of A = P(A) : P(A’)
Against A = P(A’):P(A)
INDIRECT METHOD
n(A) = n(S) – n(A’)
P(A) = 1-P(A’)
PERMUTATIONS FOR IDENTICAL OBJECTS:
n(A)=
n!
a!b!c!...
NUMBER OF SUBSETS of a SET
nC0
+ nC1 + … + nCn = 2n
nC1
+ … + nCn = 2n-1
BINOMIAL EXPANSION
(x+y)n = nC0 xn y0 + nC1 xn-1 y1+…+ nCn x0 yn
MUTUALLY EXCLUSIVE: P(A or B) = P(A) + P(B)
NON-MUTUALLY EXCLUSIVE: P(A or B) = P(A) + P(B) – P(A and B)
INDEPENDENT EVENTS: P(A and B) = P(A) x P(B)
DEPENDENT EVENTS: P(A and B) = P(A) x P(B|A)
EXPECTED VALUE: 𝐸(𝑋) = ∑ 𝑥𝑖 ∙ 𝑃(𝑥)
______________________________________________________________
1
UNIFORM DISTRIBUTION: 𝑃(𝑥) = 𝑛
1
EXPECTED VALUE: 𝐸(𝑋) = 𝑛 ∑ 𝑥𝑖
______________________________________________________________
BINOMIAL DISTRIBUTION: 𝑃(𝑥) =𝑛 𝐶𝑥 𝑝 𝑥 𝑝𝑛−𝑥
Expected Value: E(x) = np
_________________________________________________________________
HYPERGEOMETRIC DISTRIBUTION: 𝑃(𝑥) =
𝑎𝐶𝑥 ∙𝑛−𝑎 𝐶𝑟−𝑥
𝑛𝐶𝑟
HINT: solve like typical “combinations” problems
𝑟𝑎
Expected value: 𝐸(𝑋) = 𝑛
MEAN: 𝜇 =
∑ 𝑥𝑖
𝑁
Mean for weighted data: 𝜇 =
Mean for grouped data: 𝜇 =
Standard Deviation:  
𝑝
∑ 𝑤𝑖 𝑥𝑖
∑ 𝑤𝑖
∑ 𝑓𝑖 𝑚𝑖
∑ 𝑓𝑖
 X  x 
N
Percentile Rank = R = 100 (𝑛 + 1)
Percentile = p = 100
IQR = Q3 – Q1
𝐿+0.5𝐸
𝑛
2
Z-score: z 
X 

MDM4U – Residual Plots using Graphing Calculators
The overall steps for creating a residual plot are:
1. Reset your calculator
o First try: PRGM > RESET > ENTER > ENTER
o If that doesn’t work: 2ND > + > 7 > 1 > 2 > ENTER
2. Put your x and y values into lists
o STAT > EDIT > Input your data into L1 and L2
3. Create a scatter plot
o Display plot 1: 2ND > Y= > ENTER on plot 1 > Turn it on
o Change the scale to fit our data: ZOOM > ZoomStat > ENTER
4. Perform linear regression
o Make sure the r-value will display 2ND > 0 > DiagnosticOn > ENTER > ENTER
o Find equation of the line: STAT > CALC > LinReg(ax+b) > 2ND > 1 > , > 2ND > 2 > , > VARS > YVARS > 1 > 1 > ENTER
5. Graph your line of best fit
o You already put in the equation of the line of best fit by doing the “Vars” stuff above, you can
see the equation by pressing Y= and you can see the scatter plot with the line by pressing GRAPH
6. Hide your first plot and line of best fit, then plot the residuals
o Hide plot 1: 2ND > Y= > ENTER on plot 1 > Turn it off
o Hide line of best fit: Y= > move curser to equals sign and press ENTER
o Plot residuals: 2ND > Y= > ENTER on plot 2 > Turn it on > go to Ylist: > 2ND > STAT > RESID >
ZOOM > ZoomStat > ENTER
7. Remove outliers (if applicable)
o STAT > EDIT > Delete the x and y entry for the outlier, then repeat steps 3-6