If i am correct than i say the answer is B<span />
Answer:
La respuesta podría ser 80000 y en cualquier momento.
*Hint: When something is reflected across the y-axis, the rule is (-x, y).
So, you would apply that rule to the coordinate of U. All you do is change the x for a negative number and keep the y as is.
Therefore, the answer would be (-2, -2).
(i) The mean is
![\displaystyle E(X) = \sum_x x \, P(X = x) \\\\ E(X) = 1\cdot0.175 + 2\cdot0.315 + 3\cdot0.211 + 4\cdot0.092 + 5\cdot0.207 \\\\ \boxed{E(X) = 2.839}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20E%28X%29%20%3D%20%5Csum_x%20x%20%5C%2C%20P%28X%20%3D%20x%29%20%5C%5C%5C%5C%20E%28X%29%20%3D%201%5Ccdot0.175%20%2B%202%5Ccdot0.315%20%2B%203%5Ccdot0.211%20%2B%204%5Ccdot0.092%20%2B%205%5Ccdot0.207%20%5C%5C%5C%5C%20%5Cboxed%7BE%28X%29%20%3D%202.839%7D)
The variance is
![V(X) = E((X - E(X))^2) = E(X^2) - E(X)^2](https://tex.z-dn.net/?f=V%28X%29%20%3D%20E%28%28X%20-%20E%28X%29%29%5E2%29%20%3D%20E%28X%5E2%29%20-%20E%28X%29%5E2)
Compute the second moment
:
![\displaystyle E(X^2) = \sum_x x^2 \, P(X = x) \\\\ E(X) = 1^2\cdot0.175 + 2^2\cdot0.315 + 3^2\times0.211 + 4^2\times0.092 + 5^2\times0.207 \\\\ E(X^2) = 9.997](https://tex.z-dn.net/?f=%5Cdisplaystyle%20E%28X%5E2%29%20%3D%20%5Csum_x%20x%5E2%20%5C%2C%20P%28X%20%3D%20x%29%20%5C%5C%5C%5C%20E%28X%29%20%3D%201%5E2%5Ccdot0.175%20%2B%202%5E2%5Ccdot0.315%20%2B%203%5E2%5Ctimes0.211%20%2B%204%5E2%5Ctimes0.092%20%2B%205%5E2%5Ctimes0.207%20%5C%5C%5C%5C%20E%28X%5E2%29%20%3D%209.997)
Then the variance is
![\boxed{V(X) \approx 1.9171}](https://tex.z-dn.net/?f=%5Cboxed%7BV%28X%29%20%5Capprox%201.9171%7D)
(ii) For a random variable
, where
are constants, we have
![E(Z) = E(aX+b) = E(aX) + E(b) = a E(X) + b](https://tex.z-dn.net/?f=E%28Z%29%20%3D%20E%28aX%2Bb%29%20%3D%20E%28aX%29%20%2B%20E%28b%29%20%3D%20a%20E%28X%29%20%2B%20b)
and
![V(Z) = E((aX+b)^2) - E(aX+b)^2 \\\\ V(Z) = E(a^2 X^2 + 2ab X + b^2) - (a E(X) + b)^2 \\\\ V(Z) = a^2 (E(X^2) - E(X)^2) \\\\ V(Z) = a^2 V(X)](https://tex.z-dn.net/?f=V%28Z%29%20%3D%20E%28%28aX%2Bb%29%5E2%29%20-%20E%28aX%2Bb%29%5E2%20%5C%5C%5C%5C%20V%28Z%29%20%3D%20E%28a%5E2%20X%5E2%20%2B%202ab%20X%20%2B%20b%5E2%29%20-%20%28a%20E%28X%29%20%2B%20b%29%5E2%20%5C%5C%5C%5C%20V%28Z%29%20%3D%20a%5E2%20%28E%28X%5E2%29%20-%20E%28X%29%5E2%29%20%5C%5C%5C%5C%20V%28Z%29%20%3D%20a%5E2%20V%28X%29)
Then for
, we have
![E(Y) = \dfrac12 E(X) + \dfrac32 \\\\ \boxed{E(Y) = 2.918}](https://tex.z-dn.net/?f=E%28Y%29%20%3D%20%5Cdfrac12%20E%28X%29%20%2B%20%5Cdfrac32%20%5C%5C%5C%5C%20%5Cboxed%7BE%28Y%29%20%3D%202.918%7D)
![E(Y^2) = E\left(\left(\dfrac{X+3}2\right)^2\right) = \dfrac14 E(X^2) + \dfrac32 E(X) + \dfrac94 \\\\ \boxed{E(Y^2) \approx 9.0028}](https://tex.z-dn.net/?f=E%28Y%5E2%29%20%3D%20E%5Cleft%28%5Cleft%28%5Cdfrac%7BX%2B3%7D2%5Cright%29%5E2%5Cright%29%20%3D%20%5Cdfrac14%20E%28X%5E2%29%20%2B%20%5Cdfrac32%20E%28X%29%20%2B%20%5Cdfrac94%20%5C%5C%5C%5C%20%5Cboxed%7BE%28Y%5E2%29%20%5Capprox%209.0028%7D)