10. (1 ponto) Considere a seguinte função definida em partes. f (x) = { 0 se x < 0, Cx se 0 ≤ x < 0.3, 2.86(1 − x) se 0.3 ≤ x < 1, 0 se x ≥ 1. Caso...
a) 0.30
b) 2.86
c) 8.00
d) 0.60
e) 6.67
💡 1 Resposta
Ed 
Para que a função \( f(x) \) seja de fato uma densidade, a área sob a curva da função deve ser igual a 1. No caso da distribuição triangular, a área é calculada como a base vezes a altura dividido por 2. Para a região \( 0 \leq x < 0.3 \), a área é dada por \( \frac{Cx \times 0.3}{2} = \frac{0.3C}{2} = 0.15C \). Para a região \( 0.3 \leq x < 1 \), a área é dada por \( \frac{2.86(1-x) \times (1-0.3)}{2} = \frac{2.86(1-x) \times 0.7}{2} = 1 - 1.001x + 0.00143x^2 \). Somando as duas áreas, temos que a área total deve ser igual a 1: \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.00143x^2 = 1 \] \[ 0.15C + 1 - 1.001x + 0.
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