We want to separate signal events (S) from background events (B). We can simulate both types of events and check their distributions in two dimensions, x and y. S and B have the means vectors μs and ПB and the covariance matrices Vs and VB in the two dimensions, x and y: 1 = = ( 4.0 ), μB = ( 20 ) . Vs = 3- (32). - (1 ½). VB = 22 12 a) Compute the coefficients of a Fisher discriminant to classify the data into signal S and background B. b) Simulation of signal and background have produced the following five signal and five back- ground events: c) signal: y -0.28 3.48 1.30 4.52 -2.62 1.66 0.94 4.81 -1.13 3.53 background: X y 2.78 0.84 1.75 2.31 2.62 2.71 0.39 0.05 2.00 2.14 Calculate the fisher discrimimant for the events and state a possible cut to distinguish signal and background. The following five data events have been collected: X y 1.21 0.21 -0.05 0.40 -0.82 2.29 -1.31 2.35 2.32 1.42 Calculate the 95% CL upper limit on the number of signal events which pass the selection.
We want to separate signal events (S) from background events (B). We can simulate both types of events and check their distributions in two dimensions, x and y. S and B have the means vectors μs and ПB and the covariance matrices Vs and VB in the two dimensions, x and y: 1 = = ( 4.0 ), μB = ( 20 ) . Vs = 3- (32). - (1 ½). VB = 22 12 a) Compute the coefficients of a Fisher discriminant to classify the data into signal S and background B. b) Simulation of signal and background have produced the following five signal and five back- ground events: c) signal: y -0.28 3.48 1.30 4.52 -2.62 1.66 0.94 4.81 -1.13 3.53 background: X y 2.78 0.84 1.75 2.31 2.62 2.71 0.39 0.05 2.00 2.14 Calculate the fisher discrimimant for the events and state a possible cut to distinguish signal and background. The following five data events have been collected: X y 1.21 0.21 -0.05 0.40 -0.82 2.29 -1.31 2.35 2.32 1.42 Calculate the 95% CL upper limit on the number of signal events which pass the selection.
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:We want to separate signal events (S) from background events (B). We can simulate both types
of events and check their distributions in two dimensions, x and y. S and B have the means
vectors μs and ПB and the covariance matrices Vs and VB in the two dimensions, x and y:
1
=
= ( 4.0 ),
μB
= ( 20 ) .
Vs
=
3- (32). - (1 ½).
VB
=
22
12
a) Compute the coefficients of a Fisher discriminant to classify the data into signal S and
background B.
Transcribed Image Text:b) Simulation of signal and background have produced the following five signal and five back-
ground events:
c)
signal:
y
-0.28
3.48
1.30
4.52
-2.62
1.66
0.94
4.81
-1.13
3.53
background:
X
y
2.78
0.84
1.75
2.31
2.62
2.71
0.39
0.05
2.00
2.14
Calculate the fisher discrimimant for the events and state a possible cut to distinguish signal
and background.
The following five data events have been collected:
X
y
1.21 0.21
-0.05 0.40
-0.82 2.29
-1.31 2.35
2.32 1.42
Calculate the 95% CL upper limit on the number of signal events which pass the selection.
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