Using a TextView

<TextView
	android:text="Happy Birthday!"
	android:background="@android:color/darker_gray"
	android:layout_width="150dp"
	android:layout_height="75dp" />

-weird angle brackets
-don’t know what “android:text” means
-says Happy Birthday which appears on phone

XML Syntax

<LinearLayout
	android:layout_width="wrap_content"
	android:layout_height="wrap_content"
	android:orientation="vertical">

	<TextView
		android:text="Happy Birthday"
		android:layout_width="wrap_content"
		android:layout_height="wrap_content" />

	<TextView
		android:text="You're the best!"
		android:layout_width="wrap_content"
		android:layout_height="wrap_content" />

</LinearLayout>

Attribute Name, Attribute value in “Quotations”
TextView has default values if you’re ok with default values, don’t set them here.

negative correlation

How much two variable related each other.
always use correlation in statistic.
x= 3, 4, 5
y= 8, 5, 3

r = Σi[(xi-x)(yi-y)] / √Σi[(xi-x)(yi-y)]
x=1/N　Σ Xi
y=1/N　Σ Yi

x-x -1, 0, 1
y-y 3, 0, -3

= -6 / √ 2 * 18
= -1

x= 3, 4, 5
y= 8, 5, 8
r= 0

x= 3, 4, 5 xμ = 4
y= 8, 3, 7 yμ = 6

x-x -1, 0, 1
y-y 2, -3, 1

= -1 / √ 2 * 14
=　-0.189

Correlation

Correlation
r = 1 positive linear
r = 0 no relation within the data
r = -1 negative linear

b = 4
a = -3
y = 4x – 3
r is positive

correlation efficient
value between -1 and 1

r = Σi[(xi-x)(yi-y)] / √Σi[(xi-x)(yi-y)]
x=1/N　Σ Xi
y=1/N　Σ Yi

if it is
x 3, 4, 5
y 7, 8, 9

2 / √2 * 2 = 1
we know r is between -1 and 1.

x= 3, 4, 5
y= 2, 5, 8
x-x -1, 0, 1
y-y -3, 0, 3

= 6 / √ 2 * 6
= 1

Hypothesis Testing

sample -> statistic -> information -> statistic -> decision

weight loss 90% guaranteed
Yes 11, No 4
H0: p = 0.9
H1: p < 0.9 critical regions Null hypothesis [python] from math import sqrt def mean(l); return float(sum(l))/len(l) def var(l): m = mean(l) return sum([(x-m)**2 for x in l])/len(l) def factor(l): return 1.96 def conf(l): return factor(l) * sqrt(val(l)/ len(l)) def test(l, h): m = mean(l) c = conf(l) return abs(h-m) <= c l = [199, 200, 201, 202, 203, 204] print mean(l) print conf(l) [/python] 95% confidence candidate A 55 candidate B 45 1.96√p(1-p)/n = 1.96√.55-.44/100 = 9.75 Candidate A: 55 +/- 9.75

Estimation probability

Confidence　Intervals

60% partyA +-3% -> confidence interval 57, 63 in %.
many often confidence interval become 95% chance.

suppose we increase the sample size N, size of CI shrink.

P=0.5, μ=0.5, σ^2=0.25
mean(ΣXi), Var(ΣXi), Var(1/nΣXi),　std dev, CI
n=1, 0.5, 0.25, 0.25, 0.5, 0.98
n=2, 1, 0.5, 0.125, 0.35, 0.69
n=10, 5, 2.5, 0.025, 0.16, 0.31
1.96 magic number

π 3.14
e 2.718

calculate mean

# remove outliers
# extract data between lower and upper quartile

# fit Gaussian using MLE

# compute x that corresponds to standard score z
return x

import random
from math import sqrt

def mean(data):
	return sum(data)/len(data)

def variance(data):
	mu=mean(data)
	return sum([(x-mu)**2 for x in data])/len(data)

def stddev(data):
	return sqrt(variance(data))

weight=[80.,85,200,85,69,65,68,66,85,72,85,82,65,105,75,80,
    70,74,72,70,80,60,80,75,80,78,63,88.65,90,89,91,1.00E+22,
    75,75,90,80,75,-1.00E+22,-1.00E+22,-1.00E+22,86.54,67,70,92,70,76,81,93,
    70,85,75,76,79,89,80,73.6,80,80,120,80,70,110,65,80,
    250,80,85,81,80,85,80,90,85,85,82,83,80,160,75,75,
    80,85,90,80,89,70,90,100,70,80,77,95,120,250,60]

print mean(weight)

def calculate_weight(data, z):
	data.sort()
	lowerq = (len(data)-3)/4
	upperq = lowerq * 3 + 3
	newdata = [data[i] for i in range(lowerq, upperq)]

	mu = mean(newdata)
	sigma = stddev(newdata)

	x = mu + z * sigma
	return x

print calculate_weight(weight, -2.)

central limit theorem

coin:(0,1) P(Σi=k)= n!/(n-k)!k!
Pascal Triangle

flip a coin 1000 times
mean
standard deviation

import random
from math import sqrt

def mean(data):
	return float(sum(data))/len(data)

def variance(data):
	mu=mean(data)
	return sum([(float(x)-mu)**2 for x in data])/len(data)

def stddev(data):
	return sqrt(variance(data))

def flip(N):
    return [random.random() > 0.5 for x in range(N)]

N=1000
f=flip(N)

print mean(f)
print stddev(f)