Please could you help with this.
The question says that we have a 2-point mixture dist with 0.6 a SPP(α=3,θ=10) and 0.4 a SPP(α=2,θ=10). We want the Ε( Χ / Χ>20).
I tried to solve it using
Ε( Χ / Χ>20) = 0.6 Ε( Χ / Χ>20) + 0.4 Ε( Χ / Χ>20)
using the formulas for the first conditional moment of a SPP(α=3,θ=10) and for the second of a SPP(α=2,θ=10).
Also I used Ε( Χ / Χ>20) = { E(X) - E(X^20) + 20P(X>20) } / P(X>20)
And using all these end up getting a value of 34 (34 = 0.6 * 30 + 0.4 * 40).
However the right answer is 35.71 and Mahler solves it using calculus. Why is my approach not valid??
Thanks
The question says that we have a 2-point mixture dist with 0.6 a SPP(α=3,θ=10) and 0.4 a SPP(α=2,θ=10). We want the Ε( Χ / Χ>20).
I tried to solve it using
Ε( Χ / Χ>20) = 0.6 Ε( Χ / Χ>20) + 0.4 Ε( Χ / Χ>20)
using the formulas for the first conditional moment of a SPP(α=3,θ=10) and for the second of a SPP(α=2,θ=10).
Also I used Ε( Χ / Χ>20) = { E(X) - E(X^20) + 20P(X>20) } / P(X>20)
And using all these end up getting a value of 34 (34 = 0.6 * 30 + 0.4 * 40).
However the right answer is 35.71 and Mahler solves it using calculus. Why is my approach not valid??
Thanks
Mahler PE17 Q17