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Maslowich
3 years ago
6

Suppose that two teams play a series of games that ends when one of them has won ???? games. Also suppose that each game played

is won by team ???? with probability p, independent of all other games. Find the expected number of games that are played when
Mathematics
1 answer:
Musya8 [376]3 years ago
6 0

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.

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The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDE
alex41 [277]

Answer:

D,E

Step-by-step explanation:

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4 0
3 years ago
In the sequence – 40, –33, –26, –19, … determine the 77th term and the sum of the first 90 terms.
Gala2k [10]
The 77th term is 532 because the nth term is 7n-7

7x77=539

539-7=532
5 0
3 years ago
A chef uses 3 3/4 pounds of semolina flour and 1 5/8 pound whole wheat flour for each batch of pasta she makes.one week she uses
Maurinko [17]
It is to be noted that for this item, we more concern of the pounds of flour. The number of batches is calculated by dividing the total mass of flour used by the amount per batch. That is,
                                              n = 86 lbs / (1 + 5/8 lbs/batch)
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4 0
3 years ago
Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm3, what is the v
disa [49]

Answer:

Option A  V_B=19\ cm^3

Step-by-step explanation:

The volume of a cone is:

V_B = \pi\frac{hr ^ 2}{3}

The volume of a cylinder is:

V_A = \pi(r ^ 2)h

Both figures have the same height h and the same radius r.

The volume of the cylinderV_A = 18\pi\ cm ^ 3

We want to find the volume of the cone.

Then, we find r and h:

V_A = 18\pi = \pi(r ^ 2)h

We simplify.

V_A = 18 = (r ^ 2)h

Then the product of (r ^ 2)h = 18.

We substitute this in the cone formula and get:

V_B =\frac{\pi}{3}(18)\\\\V_B = \frac{18}{3}\pi\\\\V_B=19\ cm^3

8 0
3 years ago
Read 2 more answers
When f(x)=5x^2-2x+5, evaluate f(-3)
patriot [66]

Answer:

f(-3)=56

Step-by-step explanation:

When evaluating a specific input for a function, you just plug that input in for x.

So in this case, f(-3)=5(-3)^2-2(-3)+5

f(-3)=5(-3)^2-2(-3)+5

f(-3)=5(9)+6+5

f(-3)=45+6+5

f(-3)=56

8 0
2 years ago
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