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https://github.com/szymon-jozef/ZUT-notatki.git
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112 lines
2.0 KiB
R
112 lines
2.0 KiB
R
# zadanie 1, kwantyle | kolokwium
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# a)
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# kwantyl rozkładu normalnego standaryzowanego N(0,1)
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qnorm(0.97, 0, 1) # 1.880794
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qnorm(0.97) # 1.880794 | wartości 0,1 są domyślne, więc wynik jest taki sam
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# b)
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qchisq(0.975, 9) # 19.02277
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# c)
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qt(0.95, 9) # 1.833113
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# d)
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qf(0.995, 10, 23) # 3.642008
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# zadanie 2
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# a)
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pnorm(2.5, 1.5, 2) # 0.6914625
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round(pnorm(2.5, 1.5, 2), 4) # zaokrąglony wynik do 4 miejsc po przecinku: 0.6915
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# b)
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round(pnorm(-0.5, 1.5, 2, F), 4) # 0.8413
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# c)
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round(pnorm(2, 1.5, 2) - pnorm(0.5, 1.5, 2), 4) # 0.2902
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# d) na kolokwium będzie z abs
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round(pnorm(5, 1.5, 2) - pnorm(-1, 1.5, 2),4) # 0.8543
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# e)
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round(pnorm(-0.5, 1.5, 2) + pnorm(0.5,1.5,2, F),4) # 0.8501
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# f)
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# |2x - 1| < 1
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# -1 < 2x - 1 < 1
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# 0 < 2x < 2
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# 0 < x < 1
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round(pnorm(1, 1.5, 2) - pnorm(0, 1.5 ,2),4) # 0.1747
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# g)
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# |3x - 1| > 2
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# 3x - 1 < -2 && 3x -1 > 2
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# 3x < -1 && 3x > 3
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# x < -1/3 && x > 1
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round(pnorm(-1/3, 1.5, 2) + pnorm(1, 1.5, 2, F), 4) # 0.7784
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# zadanie 3
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# na kolokwium będzie b) i d)
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# a)
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# 2x > -4.5
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# 2 > -2.25
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round(pnorm(-2.25, -4, 3.5, F), 4) # 0.3085
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# b)
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# |5x - 1| > 2.5
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# 5x - 1 < -2.5 || 5x - 1 > 2.5
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# 5x < -1.5 || 5x > 3.5
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# -0.3 < -0.75 || x > 0.7
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round(pnorm(-0.3, -4, 3.5) + pnorm(0.7, -4, 3.5, F), 4) # 0.9444
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# c)
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# -8 < 3x + 1 < 2
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# -9 < 3x < 1
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# -3 < x < 1/3
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round(pnorm(1/3, -4, 3.5) - pnorm(-3, -4, 3.5), 4) # 0.2797
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# d)
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pnorm(7.5/4, -4, 3.5) - pnorm(-3.5/4, -4, 3.5) #0.139349
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# zadanie 4 | N(1000, 50)
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# a)
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round(pnorm(900, 1000, 50) * 4000) # 91
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# b)
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qnorm(0.13, 1000, 50, F) # 1056.32
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# zadanie 5 | N(6.8, 0.3)
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# a)
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round(pnorm(7.1, 6.8, 0.3) * 30) # 25
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# b)
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qnorm(0.15, 6.8, 0.3) # 6.48907
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# zadanie 6 | N(15, 13)
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# a) 22,05 < x < 22,10
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(pnorm(10,15,13)-pnorm(5,15,13)) # 0.129383
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# b)
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pnorm(20,15,13,F) # 0.3502612
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# zadanie 7 | N(20,5)
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#a) p = 0.8849 X < k1
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qnorm(0.8849, 20, 5)
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#25.99922
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#b) p =0.6554 X > k2
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qnorm(0.6554, 20, 5, F)
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#18.0003
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# c)
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20 - qnorm((1 - 0.6554) / 2, 20, 5) # 4.725577
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# d)
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20 - qnorm(0.00511/2, 20, 5) #14.00008
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