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https://github.com/szymon-jozef/ZUT-notatki.git
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75 lines
1.2 KiB
R
75 lines
1.2 KiB
R
# zadanie 1
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# a)
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# P(x > 5) = 70 / 200
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x_5 = 70 / 200
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# P(x <= 5) = 1 - x_5
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x_5_F = 1 - x_5
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sigma = 1
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# (5 - m) / sig = qnorm(1 - 70/200)
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m = 5 - sigma * qnorm(x_5_F)
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round(pnorm(6, m, sigma) - pnorm(3, m, sigma), 4) # 0.8638
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# b)
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# P(x < 6) = 0.8
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x_6 = 0.8
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wariancja = 4
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sigma = sqrt(wariancja) # 2
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# (6 - m) / sigma = qnorm(0.8)
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m = 6 - qnorm(0.8) * sigma
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round(pnorm(6, m, sigma) - pnorm(3, m , sigma), 4) # 0.5449
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# zadanie 2
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m = 5.2 # w procentach
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# P(x < 3) = 12.1%
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P_x = 0.121
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# (3 - m) / sigma = qnorm(P_x)
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sigma = (3 - m)/qnorm(P_x)
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print(sigma) # 1.880338
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qnorm(0.8, m, sigma) # 6.782532%
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# zadanie 3
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m = -5
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# P( X < -2) = 0.95
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sig = (-2 - m)/qnorm(0.95)
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sig # 4.255698
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# P(X > 0)
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pnorm(0, m, sig, F) # 0.003058688
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# zadanie 4
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# aby zdać: ponad 50%
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# pierwszy termin: średnio: 46%, zdawalność: 40%
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# a)
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# P(X > 0.7) = ?
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a = 0.7
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m = 0.46
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sigma = (0.5 - m)/qnorm(0.6)
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pnorm(0.7, m, sigma, F)
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# b)
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qnorm(0.1, m, sigma, F)
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# zadanie 5
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sigma = 0.12
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# P(x > 0.8) = 3/12
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P_x = 3/12
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# (0.8 - m) / sigma = qnorm(3/12)
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m = 0.8 - qnorm(1 - P_x) * sigma
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qnorm(0.1, m, sigma, F) # 0.8728474
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# zadanie 6
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m = 86.5
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P_x = 0.3472
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a = 82.5
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sigma = (a - m)/qnorm((1 - P_x)/2)
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round(pnorm(95, m, sigma, F) * 400) # 68
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