1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
PLEASE HELP !!!!!!! GEOMETRY
nata0808 [166]
I came up with d and e as an answer
6 0
3 years ago
Which of the following represents "five times the sum of a number and fifteen is fifty"?
Kisachek [45]
Yes, the correct answer is A because you're multiplying 5 by the expression (N+15)
6 0
3 years ago
Read 2 more answers
Which expressions are equivalent to 16 x 4 minus 64 check all that apply
Reika [66]
Oof I was going to answer this but it got me confusion.
3 0
3 years ago
Read 2 more answers
A measurement that closely agrees with accepted values
bixtya [17]

A measurement that closely agrees with an accepted value is best described as a numerical

3 0
3 years ago
Find the radius and the diameter to the nearest hundredth when C = 7π yd. Use 3.14 for π.
valentinak56 [21]

Answer:

Diameter = 7

Radius = 3.5

Step-by-step explanation:

Hi! Ace here.

So, the formula to find circumference is dπ or 2rπ

So to find the diameter, you do the circumference/π

To find the radius, you'd do the circumference/2π

Plug-in those numbers and there you go!

Hope this helps, let me know if you have any questions.

I know this was a very vague explanation so I encourage you to ask any questions. Thank you!

5 0
2 years ago
Other questions:
  • how do you graph a exponential function , such as the following, without a calculator: f(x)= -3(2)^x-3+1
    10·1 answer
  • What property is m+7=7+m
    13·1 answer
  • You are shipping a box that weighs 5 pounds. Shipping charges are listed by ounces at the local mail center. The first ounce cos
    6·2 answers
  • What is the value of x? Enter your answer in the box.
    6·2 answers
  • Please help me guys!
    13·1 answer
  • -2(-1x + 5y) + 3(2x - 6y) Use distributive property and combine like terms to solve *
    9·1 answer
  • Evaluate -8 × |2|.<br><br> A)-10<br> B)10<br> C)-16<br> D)16
    7·2 answers
  • Eighteen technicians in a cell phone repair shop are randomly selected to participate in a study comparing two screen repair tec
    15·1 answer
  • Some studies show that high school students are more successful when the school day begins after 9 am. To test this theory,
    10·1 answer
  • There are 120 people in a sport centre.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!