Answer:
(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0
(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0
Step-by-step explanation:
(a) when i = 2, the expected number of played games will be:
E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] = 4p²-4p+2-6p²+6p = -2p²+2p+2.
If p = 1/2, then:
d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.
(b) when i = 3;
E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]
Simplification and rearrangement lead to:
E(X) = 6p⁴-12p³+3p²+3p+3
if p = 1/2, then:
d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10
Therefore, E(X) is maximized.
Answer:
All real solutions
Step-by-step explanation:
- The given graph is a maximum quadratic function.
- The solution to the graph is where the graph intersects the x-axis.
- We can see from the graph that, the function intersected the x-axis at two different points, hence its discriminant is greater than zero.
- Hence the solution of g(x) are two distinct real solutions.
- The solutions are not whole numbers because the x-intercepts are not exact.
- The solutions are also not all points that lie on g(x)
- The first choice is correct.
<em>The Ordered pair of solution will be (x,y)=(2,3)</em>
<h3>Steps below⤵️</h3>
- Solve the second equation for y
- Substitute the given value of y into the first equation
- Solve the first equation for x
- Substitute the given value of x into the second equation
- Solve the equation for y
- The possible solution of the system is the ordered pair (x,y)
- And we are done solving!!~
Answer:
$20 i think
Step-by-step explanation: have a good day bye bye yup yup
