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.
Given the compound statement <span>(p∨q)∧r
where: p: 5 < -3
q : All vertical angles are congruent.
r: 4x = 36, then x = 9.
Recall the in logic, '</span>∨' symbolises "or" while '∧' symbolises "and".
Therefore, the compound statement <span>(p∨q)∧r can be written as follows:
Either 5 < -3 or all vertical angles are congruent, and if 4x = 36, then x = 9.
</span>
Answer: 219.8 meters
Step-by-step explanation:
Since his stride measures 1.4 meters and the length of the field is 157 strides, then the length of the stride in meters is 157*1.4 meters.
= 219.8 meters
Answer:
y = 30x + 75
Step-by-step explanation:
every month you're paying 30 dollars for a fee.
the 75 dollars is simply the "down payment" so to say.
m is the constant growth or the continuous growth or the charge per month.
