BFN/bfn - Technical University of Denmark · IMM - DTU 02405 Probability 2005-3-11 BFN/bfn Question...
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IMM - DTU 02405 Probability 2005-3-11 BFN/bfn Question a) # of days 28 30 31 frequency
Transcript of BFN/bfn - Technical University of Denmark · IMM - DTU 02405 Probability 2005-3-11 BFN/bfn Question...
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency
1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1
4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) =
28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 ·
1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+
30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) =
282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 28
2 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 ·
1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+
302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 ·
4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =
√E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)
− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 =
0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency
28365
120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365
120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) =
28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) =
282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 ·
28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+
302 · 120365
+ 312 · 217365
=338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =
√E(X2)− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)
− E(X)2 = 0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 =
0.841
IMM - DTU 02405 Probability
2005-3-11BFN/bfn
Question a)# of days 28 30 31frequency 1 4 7
E(X) = 28 · 1
12+ 30 · 4
12+ 31 · 7
12=
365
12= (30.42)
E(X2) = 282 · 1
12+ 302 · 4
12+ 312 · 7
12
SD(X) =√
E(X2)− E(X)2 = 0.86
Question b)# of days 28 30 31frequency 28
365120365
217365
E(X) = 28 · 28
365+ 30 · 120
365+ 31 · 217
365=
11111
365
E(X2) = 282 · 28
365+ 302 · 120
365+ 312 · 217
365=
338489
365
SD(X) =√
E(X2)− E(X)2 = 0.841
