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
Advocard [28]
2 years ago
9

Let Xn be the random variable that equals the number of tails minus the number of heads when n fair coins are flipped. What is t

he expected value of Xn? What is the variance of Xn?
Mathematics
1 answer:
Firlakuza [10]2 years ago
4 0

Answer:

the expected value of Xn , E(Xn) = 0 and the variance σ²(Xn) = n*(1-2n)

Step-by-step explanation:

If X1= number of tails when n fair coins are flipped , then X1 follows a binomial distribution with E(X1) = n*p , p=0,5 and the number of heads obtained is X2=n-X1

therefore

Xn =X1-X2 = X1- (n-X1) = 2X1-n

thus

E(Xn) =∑ (2*X1-n) p(X1) =  2*∑[X1 p(X1)] -n∑p(X1) = 2*E(X1)-n = 2*n*p--n= 2*n*1/2 -n = n-n =0

the variance will be

σ²(Xn) = ∑ [Xn - E(Xn)]² p(Xn) = ∑ [(2X1-n) - 0 ]² p(X1) = ∑ (4*X1²-4*X1*n+n²) p(X1) = = 4*∑ X1²p(X1) - 4n ∑X1 p(X1) -  n²∑p(X1) = 2*E(X1²) -4n*E(X1)- n²

since

σ²(X1) = n*p*(1-p) = n*0,5*0,5=n/4

and

σ²(X1) = E(X1²) - [E(X1)]²

n/4 = E(X1²) - (n/2)²

E(X1²) = n(n+1)/4

therefore

σ²(Xn) = 4*E(X1²) -4n*E(X1)- n² = 4*n(n+1)/4 - 4*n*n/2 - n² = n(n+1) - 2n² - n²

= n - 2n² = n(1-2n)

σ²(Xn) = n(1-2n)

You might be interested in
Z-2w=2 please help me solve , studying for praxis
RUDIKE [14]

Answer:

Z(2w-2)=24

Simple and best practice solution for Z(2w-2)=24 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

5 0
2 years ago
1 1/2× 3/4 please answer
Lynna [10]
It is 3/2 • 3/4 because you have to make the mixed number an improper fraction. Theb you would solve 3/2 • 3/4 and get 9/8 and that simplified is 1 1/8
6 0
3 years ago
Read 2 more answers
What is 100 divided by 2
LenaWriter [7]
50 Is the answer.........
4 0
3 years ago
Read 2 more answers
Which of these numbers is an irrational numbers​
Aliun [14]

Answer:square root of 25 square root of 4

Step-by-step explanation:

8 0
2 years ago
Find the slope of the line containing the points (5, -1) and (-8, -4).
UkoKoshka [18]
I think it might be D
7 0
2 years ago
Other questions:
  • Simplify this equation ASAP please
    11·1 answer
  • A rocket is launched into the air. The projectile motion of the rocket can be modeled using h(t) = 112t –16t2, where t is the ti
    8·2 answers
  • What is the exact volume of a sphere that has a radius of 8.4 in.?
    10·1 answer
  • Please help me !!!!!!!!!!
    6·1 answer
  • Jackson went outside to look at the stars at 8:40 in the evening he went back inside at 9:25 how long did Jackson look at the st
    6·1 answer
  • How many different four digit numbers can you make with these?
    14·1 answer
  • By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day. Using su
    14·2 answers
  • I need the x and y value<br><br><br> I did it and I got 26 got both, but I’m not sure.
    15·2 answers
  • Help I need the answer in 5 minutes!!
    10·2 answers
  • Natalie was out at a restaurant for dinner when the bill came. Her dinner came to $29. After adding in a tip, before tax, she pa
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!