[Graphics:Images/index_gr_1.gif]
[Graphics:Images/index_gr_2.gif]

Attenzione: 1) i comandi seguiti da ";" sono eseguiti senza visualizzare il risultato; 2) il simbolo "%" sta il risultato del comando precedente; 3) la funzione "N[ ]" obbliga a dare risultati "numerici" invece di "risultati esatti".  Tutti gli altri simboli e funzioni dovrebbero essere autoesplicativi

1)

a)

[Graphics:Images/index_gr_3.gif]

[Graphics:Images/index_gr_4.gif]
[Graphics:Images/index_gr_5.gif]
[Graphics:Images/index_gr_6.gif]
[Graphics:Images/index_gr_7.gif]
[Graphics:Images/index_gr_8.gif]
[Graphics:Images/index_gr_9.gif]
b)

[Graphics:Images/index_gr_10.gif]

[Graphics:Images/index_gr_11.gif]
[Graphics:Images/index_gr_12.gif]
[Graphics:Images/index_gr_13.gif]
[Graphics:Images/index_gr_14.gif]
[Graphics:Images/index_gr_15.gif]
[Graphics:Images/index_gr_16.gif]
c)

[Graphics:Images/index_gr_17.gif]

[Graphics:Images/index_gr_18.gif]
[Graphics:Images/index_gr_19.gif]
[Graphics:Images/index_gr_20.gif]
[Graphics:Images/index_gr_21.gif]
[Graphics:Images/index_gr_22.gif]
[Graphics:Images/index_gr_23.gif]
d)

[Graphics:Images/index_gr_24.gif]

[Graphics:Images/index_gr_25.gif]
[Graphics:Images/index_gr_26.gif]
[Graphics:Images/index_gr_27.gif]
[Graphics:Images/index_gr_28.gif]
[Graphics:Images/index_gr_29.gif]
[Graphics:Images/index_gr_30.gif]

2)

a)=b)

[Graphics:Images/index_gr_31.gif]
[Graphics:Images/index_gr_32.gif]
[Graphics:Images/index_gr_33.gif]
[Graphics:Images/index_gr_34.gif]

c)

[Graphics:Images/index_gr_35.gif]
[Graphics:Images/index_gr_36.gif]
[Graphics:Images/index_gr_37.gif]
[Graphics:Images/index_gr_38.gif]
[Graphics:Images/index_gr_39.gif]

d)

[Graphics:Images/index_gr_40.gif]
[Graphics:Images/index_gr_41.gif]
[Graphics:Images/index_gr_42.gif]

3)

a)

[Graphics:Images/index_gr_43.gif]
[Graphics:Images/index_gr_44.gif]
[Graphics:Images/index_gr_45.gif]
[Graphics:Images/index_gr_46.gif]
[Graphics:Images/index_gr_47.gif]

b)

[Graphics:Images/index_gr_48.gif]
[Graphics:Images/index_gr_49.gif]
[Graphics:Images/index_gr_50.gif]
[Graphics:Images/index_gr_51.gif]
[Graphics:Images/index_gr_52.gif]
[Graphics:Images/index_gr_53.gif]
[Graphics:Images/index_gr_54.gif]

c)

[Graphics:Images/index_gr_55.gif]
[Graphics:Images/index_gr_56.gif]
[Graphics:Images/index_gr_57.gif]
[Graphics:Images/index_gr_58.gif]
[Graphics:Images/index_gr_59.gif]

d)

[Graphics:Images/index_gr_60.gif]
[Graphics:Images/index_gr_61.gif]
[Graphics:Images/index_gr_62.gif]
[Graphics:Images/index_gr_63.gif]
[Graphics:Images/index_gr_64.gif]
[Graphics:Images/index_gr_65.gif]
[Graphics:Images/index_gr_66.gif]

4)

a)

[Graphics:Images/index_gr_67.gif]
[Graphics:Images/index_gr_68.gif]
[Graphics:Images/index_gr_69.gif]
[Graphics:Images/index_gr_70.gif]
[Graphics:Images/index_gr_71.gif]
[Graphics:Images/index_gr_72.gif]
[Graphics:Images/index_gr_73.gif]

b)

[Graphics:Images/index_gr_74.gif]
[Graphics:Images/index_gr_75.gif]
[Graphics:Images/index_gr_76.gif]
[Graphics:Images/index_gr_77.gif]
[Graphics:Images/index_gr_78.gif]
[Graphics:Images/index_gr_79.gif]
[Graphics:Images/index_gr_80.gif]
[Graphics:Images/index_gr_81.gif]
[Graphics:Images/index_gr_82.gif]

c)

[Graphics:Images/index_gr_83.gif]
[Graphics:Images/index_gr_84.gif]
[Graphics:Images/index_gr_85.gif]
[Graphics:Images/index_gr_86.gif]
[Graphics:Images/index_gr_87.gif]
[Graphics:Images/index_gr_88.gif]

b)

[Graphics:Images/index_gr_89.gif]
[Graphics:Images/index_gr_90.gif]
[Graphics:Images/index_gr_91.gif]
[Graphics:Images/index_gr_92.gif]
[Graphics:Images/index_gr_93.gif]
[Graphics:Images/index_gr_94.gif]
[Graphics:Images/index_gr_95.gif]
[Graphics:Images/index_gr_96.gif]
[Graphics:Images/index_gr_97.gif]

5)

a)

[Graphics:Images/index_gr_98.gif]
[Graphics:Images/index_gr_99.gif]
[Graphics:Images/index_gr_100.gif]
[Graphics:Images/index_gr_101.gif]
[Graphics:Images/index_gr_102.gif]
[Graphics:Images/index_gr_103.gif]
[Graphics:Images/index_gr_104.gif]
[Graphics:Images/index_gr_105.gif]

b)

[Graphics:Images/index_gr_106.gif]
[Graphics:Images/index_gr_107.gif]
[Graphics:Images/index_gr_108.gif]
[Graphics:Images/index_gr_109.gif]

c)

[Graphics:Images/index_gr_110.gif]
[Graphics:Images/index_gr_111.gif]
[Graphics:Images/index_gr_112.gif]
[Graphics:Images/index_gr_113.gif]
[Graphics:Images/index_gr_114.gif]
[Graphics:Images/index_gr_115.gif]
[Graphics:Images/index_gr_116.gif]
[Graphics:Images/index_gr_117.gif]

d)

[Graphics:Images/index_gr_118.gif]
[Graphics:Images/index_gr_119.gif]
[Graphics:Images/index_gr_120.gif]
[Graphics:Images/index_gr_121.gif]

6)

7)

a)

[Graphics:Images/index_gr_142.gif]
[Graphics:Images/index_gr_143.gif]
[Graphics:Images/index_gr_144.gif]
[Graphics:Images/index_gr_145.gif]

Quindi dev'essere μs > 0.25

b)

[Graphics:Images/index_gr_146.gif]
[Graphics:Images/index_gr_147.gif]
[Graphics:Images/index_gr_148.gif]

[Graphics:Images/index_gr_149.gif]

[Graphics:Images/index_gr_150.gif]
[Graphics:Images/index_gr_151.gif]

[Graphics:Images/index_gr_152.gif]

[Graphics:Images/index_gr_153.gif]
[Graphics:Images/index_gr_154.gif]

[Graphics:Images/index_gr_155.gif]

c)

[Graphics:Images/index_gr_156.gif]
[Graphics:Images/index_gr_157.gif]
[Graphics:Images/index_gr_158.gif]
[Graphics:Images/index_gr_159.gif]

Quindi dev'essere mm < 0.4 Kg

d)

[Graphics:Images/index_gr_160.gif]
[Graphics:Images/index_gr_161.gif]
[Graphics:Images/index_gr_162.gif]

[Graphics:Images/index_gr_163.gif]

[Graphics:Images/index_gr_164.gif]
[Graphics:Images/index_gr_165.gif]

[Graphics:Images/index_gr_166.gif]

[Graphics:Images/index_gr_167.gif]
[Graphics:Images/index_gr_168.gif]

[Graphics:Images/index_gr_169.gif]

8)

a)

[Graphics:Images/index_gr_170.gif]
[Graphics:Images/index_gr_171.gif]
[Graphics:Images/index_gr_172.gif]
[Graphics:Images/index_gr_173.gif]
[Graphics:Images/index_gr_174.gif]

b)

[Graphics:Images/index_gr_175.gif]
[Graphics:Images/index_gr_176.gif]
[Graphics:Images/index_gr_177.gif]
[Graphics:Images/index_gr_178.gif]
[Graphics:Images/index_gr_179.gif]

c)

[Graphics:Images/index_gr_180.gif]
[Graphics:Images/index_gr_181.gif]
[Graphics:Images/index_gr_182.gif]
[Graphics:Images/index_gr_183.gif]
[Graphics:Images/index_gr_184.gif]

b)

[Graphics:Images/index_gr_185.gif]
[Graphics:Images/index_gr_186.gif]
[Graphics:Images/index_gr_187.gif]
[Graphics:Images/index_gr_188.gif]
[Graphics:Images/index_gr_189.gif]

Statistica

1)

[Graphics:Images/index_gr_190.gif]
[Graphics:Images/index_gr_191.gif]
[Graphics:Images/index_gr_192.gif]

Quindi p=(24.3+-1.0)%
Per avere un risultato al 95% bisognera' considerare due sigma, ovvero p=(24.3+-2.0)%, o semplicemente p=(24+-2)%.

2)

[Graphics:Images/index_gr_193.gif]
[Graphics:Images/index_gr_194.gif]
[Graphics:Images/index_gr_195.gif]
[Graphics:Images/index_gr_196.gif]
[Graphics:Images/index_gr_197.gif]
[Graphics:Images/index_gr_198.gif]

Ovvero μ = 2.345 +- 0.012.
Al 95%:  μ = 2.345 +- 0.024.
calcoliamo P(2.34 <= μ <= 2.35) dalla distribuzione di Gauss:

[Graphics:Images/index_gr_199.gif]
[Graphics:Images/index_gr_200.gif]
[Graphics:Images/index_gr_201.gif]

Ovvero facendo numericamente l'integrale

[Graphics:Images/index_gr_202.gif]
[Graphics:Images/index_gr_203.gif]
[Graphics:Images/index_gr_204.gif]

... oppure dalle tabelle

[Graphics:Images/index_gr_205.gif]
[Graphics:Images/index_gr_206.gif]

3)

Ciascuna Xi e' uniforme con Ex=0.5 e Sigmax=1/[Graphics:Images/index_gr_207.gif]=0.29
Chiamando Y=[Graphics:Images/index_gr_208.gif]i, abbiamo che Y e' approssimativamente gaussiana con Y=[Graphics:Images/index_gr_209.gif]i = 2.5 e Var=[Graphics:Images/index_gr_210.gif]i = 0.42,

[Graphics:Images/index_gr_211.gif]
[Graphics:Images/index_gr_212.gif]
[Graphics:Images/index_gr_213.gif]
[Graphics:Images/index_gr_214.gif]
[Graphics:Images/index_gr_215.gif]

4)

Abbiamo

[Graphics:Images/index_gr_216.gif]

[Graphics:Images/index_gr_217.gif]

[Graphics:Images/index_gr_218.gif]
[Graphics:Images/index_gr_219.gif]
[Graphics:Images/index_gr_220.gif]
[Graphics:Images/index_gr_221.gif]
[Graphics:Images/index_gr_222.gif]

Il valore atteso di Y sara' dato da

[Graphics:Images/index_gr_223.gif]
[Graphics:Images/index_gr_224.gif]

Mentre

[Graphics:Images/index_gr_225.gif]
[Graphics:Images/index_gr_226.gif]

Da cui

[Graphics:Images/index_gr_227.gif]
[Graphics:Images/index_gr_228.gif]

Ovvero Y = (62 +- 4) [Graphics:Images/index_gr_229.gif].

Per capire quale delle quattro grandezze e' maggiormente responsabile dell'incertezza di Y, bisogna considerare i quattro contributi nall'incertezza relativa:

[Graphics:Images/index_gr_230.gif]
[Graphics:Images/index_gr_231.gif]
[Graphics:Images/index_gr_232.gif]
[Graphics:Images/index_gr_233.gif]
[Graphics:Images/index_gr_234.gif]

--> domina X4 .  


Converted by Mathematica      January 9, 2002