Ucas Exam - Stats And Mechanics Flashcards
Standard deviation (words)
The root of: the mean of the squares minus the square of the means
Standard deviation formula
√(Σfx^2/Σf)-(Σfx/Σf)^2
Linear interpolation formula
LB+(PL/GF x CW)
Coded data
y = (x-a)/b
Mean of coded data
ȳ = (x̄-a)/b
Standard deviation of coded data
σy = σx/b
Where to draw cross on cumulative frequency graph
Upper end point of the class width
Where to draw cross for frequency polygon
Midpoint of class width
Frequency formula
Frequency = frequency density x class width
What formula is for mutually exclusive probability events
P(A U B) = P(A)+P(B)
What formula is for statistically independent probability events
P(A n B) = P(A) x P(B)
What is the addition formula for P(A U B)
P(A) + P(B) - P(A n B)
What is the multiplication formula for P(B|A)
P(B n A)/ P(A)
Binomial PD without calc
nCr x P(failure)^no.failures x P(success)^no.success
Binomial distribution, what does each letter mean
X ~ B(n,r)
n = number of trials
p = probability of success
Binomial PD
P(X=y)
Binomial CD
P(X ≤ y)
Normal distribution p(1 sd from mean)
68%
Normal distribution p(2 sd from mean)
95%
Normal distribution p(3 sd from mean)
99.7%
Expression for normal distribution and what does each letter mean
X ~ N(μ, σ^2)
Mu = mean
σ = standard deviation
What is the probability in Inverse normal
The area to the left
What is the standard normal distribution
Z ~ N(0,1^2)
What is the formula for z in standard normal
Z = (X - μ)/σ
How to find missing mean or sd value normal distribution
Use inverse to find the Z value and sub into the formula
What is going from binomial to normal called
Continuity correction
Binomial to normal conversions
Mean - np
Variance - np(1-p)
when can a binomial distribution be approximated to a normal
p close to 0.5
n is large
conditions for binomial distribution
- fixed number of trials
- 2 possible outcomes
- fixed probability of success
- trials are independent
what does binomial distribution measure
p(X≤x)
p(B|A)
probability of b occurring given that A has already occurred
formula for p(B|A)
p(B n A)/p(A)
moment
force x distance
rigid body in equilibrium
resultant force and resultant moments = 0
maximum friction
μR
static rigid body
- stationary
- resultant force = 0
- resultant moment = 0
further kinematics - displacement (constant velocity)
r = r0 + vt
Further kinematic - constant acceleration
r = r0 + (ut + 0.5at^2)
Sample mean normal distribution
x̄ ~ N(μ, σ^2/n)
