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:
A similarity transformation is a dilation or a composition of rigid motions and dilations. Two geometric figures are similar figures if and only if there is a similarity transformation that maps one of the figures onto the other. Similar figures have the same shape but not necessarily the same size.
Step-by-step explanation:
Answer:
5 1/4
Step-by-step explanation:
I’ll teach you how to solve 3.26d+9.75d-2.65
——————————————-
3.26d+9.75d-2.65
Collect like terms by adding their coefficients:
(3.26+9.75)d-2.65
Add the numbers:
3.26+9.75= 13.01
13.01d-2.65
Your Answer Is 13.01d-2.65
Plz mark me as brainliest if this helped :)
Answer:
8.83 x 10^-5 grams
Step-by-step explanation:
3.7 x 10^-6 grams of carbon power
0.000092 grams of ammonium carbonate
0.000092 = 9.2 x 10^-5
3.7 x 10^-6 = 0.37 x 10^-5
The difference:
(9.2 x 10^-5 ) - (0.37 x 10^-5)
= (9.2 - 0.37) x 10^-5
= 8.83 x 10^-5
