math homework

2 files changed, 226 insertions, 0 deletions

diff --git a/maths/hw/wpp2/Makefile b/maths/hw/wpp2/Makefile
new file mode 100644
index 0000000..73b377f
--- /dev/null
+++ b/maths/hw/wpp2/Makefile
@@ -0,0 +1,4 @@
+all: wpp2
+
+wpp2: wpp2.ms
+	groff -ms -Tps -e wpp2.ms | ps2pdf - > wpp2.pdf
diff --git a/maths/hw/wpp2/wpp2.ms b/maths/hw/wpp2/wpp2.ms
new file mode 100644
index 0000000..6c0fff9
--- /dev/null
+++ b/maths/hw/wpp2/wpp2.ms
@@ -0,0 +1,222 @@
+.TL
+Weekly past paper 2 (stats)
+.AU
+Lucas Standen
+.AI
+QMC
+
+.AB
+.CD
+.I
+I thought for all our sanities, we might appreciate me trying to type this :)
+.AE
+
+.PP
+1)a)
+.EQ
+22 - 16 over sigma = 1.28155
+.EN
+
+.EQ
+sigma = 22 - 16 over 1.28155
+.EN
+
+.EQ
+sigma = 4.68
+.EN
+
+.PP
+1)b)
+
+.EQ
+P(L < 16) = P(Z < 13-16 over 4.68 )
+.EN
+
+.EQ
+P(L < 16) = 26.1%
+.EN
+
+.PP
+1)c)
+
+.EQ
+P(S < 8) = 0.1
+.EN
+
+.EQ
+{8 - mu} over sigma = -1.2816
+.EN
+
+.EQ
+{17 - mu} over sigma = 0.8416
+.EN
+
+.EQ
+sigma = 4.238
+.EN
+
+.EQ
+mu = 13.432
+.EN
+
+.PP
+1)d)
+.EQ
+13.4 > 16
+.EN
+
+.EQ
+"this supports thier belief"
+.EN
+
+.PP
+2)a)
+
+.EQ
+W = " The number of cards out of the 20 winning ones"
+.EN
+
+.EQ
+W " ~ " B(20, 0.45)
+.EN
+
+.EQ
+S = " The number of stores with 12 or more winning cards"
+.EN
+
+.EQ
+S " ~ " B(8, p)
+.EN
+
+.EQ
+p = P(w >= 12) = 0.1308
+.EN
+
+.EQ
+P(S >= 2) = 0.2818
+.EN
+
+.PP
+2)b)
+
+.EQ
+"There is a large number of trials, so the rate should be close 0.5"
+.EN
+
+.PP
+2)c)
+.EQ
+X " ~ " N(135, 74.25)
+.EN
+
+.EQ
+P(X < 122.5) 
+.EN
+
+.EQ
+P(Z < {122.5 - 135} over sqrt 74.25 ) = 0.0734
+.EN
+
+.PP
+2)d)
+.EQ
+"The probability is higher than 2.5% therefore there is not enough evidence to suggest that the proportion is not 45%"
+.EN
+
+.PP
+3)a)i)
+.EQ
+X " ~ " N(30, 2 sup 2 )
+.EN
+
+.EQ
+P(X = 31) = 0
+.EN
+
+.PP
+3)a)ii)
+.EQ
+P(X > 31) = 0.3085
+.EN
+
+.PP
+3)b)i)
+.EQ
+0.0668 times (1 - 0.0668) sup 4 = 0.0507
+.EN
+
+.PP
+3)b)ii)
+.EQ
+P(Y > 1) = 1 - P(Y <= 1)
+.EN
+
+.EQ
+1 - 0.9610 = 0.039
+.EN
+
+.PP
+3)c)
+.EQ
+H " ~ " N( mu , 1.5 sup 2 )
+.EN
+
+.EQ
+P(H > 42) = 0.0005
+.EN
+
+.EQ
+z = {42 - mu} over 1.5 = 3.29
+.EN
+
+.EQ
+mu = 37.06
+.EN
+
+.PP
+4)a)
+.EQ
+"mean "= 1680 over 60 = 28 " mins "
+.EN
+
+.EQ
+S sub xx =  47654.4 - 1680 sup 2 over 60 = 614.4
+.EN
+
+.EQ
+sigma = sqrt {S sub xx over 60} = 3.2
+.EN
+
+.PP
+4)b)
+.EQ
+H sub 0 : mu = 27.5
+.EN
+
+.EQ
+H sub 1 : mu > 27.5
+.EN
+
+.EQ
+z = 28 - 27.5 over {3 over sqrt 60} = 1.2909
+.EN
+
+.EQ
+z = 1.64485
+.EN
+
+.EQ
+"no sufficent evidence to support her belief"
+.EN
+
+.PP
+4)c)i)
+.EQ
+"assuming that you will always have a p of 0.2 is not likely"
+.EN
+
+.PP
+4)c)ii)
+.EQ
+"moddel the fastest and slowest people as 2 distributions"
+.EN