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:
Step-by-step explanation:
A parameter describes a population, and a statistic describes a sample.
The first one is a statistic. A sample was surveyed.
The second one is a parameter. It describes the entire soccer team.
The third one is a statistic. A sample was surveyed.
The fourth one is a parameter. It describes the entire golf team.
Answer:
45.2
Step-by-step explanation:
the tenths is the first number to the right after the decimal
Building and solving an inequality, it is found that at a volume of sales of $11,875 he will start to earn more from the commission based compensation.
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- We want to find how much in dollars he has to sell such that 8% of this amount is greater than $950.
- Supposing he sells $x, 8% of this is represented by 0.08x. We want it to be greater than $950, thus, the inequality is:
Now we solve the inequality, similarly to how we would solve an equality.
At a volume of sales of $11,875 he will start to earn more from the commission based compensation.
A similar problem is given at brainly.com/question/17248342
