• Support PF! Buy your school textbooks, materials and every day products Here!

Continuous Probability

  • Thread starter noreturn2
  • Start date
  • #1
25
0

Homework Statement


f(x) = (3/4)(-x^2 + 6x - 8) for 2 < x < 4 (0 elsewhere)

A) Find F(x)

integral 2 to 4 ((3/4)(-x^2 + 6x - 8))dx

B) Use F(x) to find P(3 < X < 3.5)

integral 3 to 3.5 ((3/4)(-x^2 + 6x - 8))dx

11/32

C) Use F(x) to find P(X > 3.5)

1-( P(3 < X < 3.5)) = 21/31

D) Find E(X).

integral 2 to 4 (x*(3/4)(-x^2 + 6x - 8))dx = 3

E) Find the standard deviation of X.

integral 2 to 4 (x^2(3/4)(-x^2 + 6x - 8))dx E[x^2)-E[x] = sqrt(6.2)= 2.48
 

Answers and Replies

  • #2
FactChecker
Science Advisor
Gold Member
5,378
1,947
They will expect you to give the formula of the integrals you mention. For the simple polynomial of this problem, you should be able to do that.
 
  • #3
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement


f(x) = (3/4)(-x^2 + 6x - 8) for 2 < x < 4 (0 elsewhere)

A) Find F(x)

integral 2 to 4 ((3/4)(-x^2 + 6x - 8))dx

B) Use F(x) to find P(3 < X < 3.5)

integral 3 to 3.5 ((3/4)(-x^2 + 6x - 8))dx

11/32

C) Use F(x) to find P(X > 3.5)

1-( P(3 < X < 3.5)) = 21/31

D) Find E(X).

integral 2 to 4 (x*(3/4)(-x^2 + 6x - 8))dx = 3

E) Find the standard deviation of X.

integral 2 to 4 (x^2(3/4)(-x^2 + 6x - 8))dx E[x^2)-E[x] = sqrt(6.2)= 2.48
(A) ##F(4) = \int_2^4 (3/4) (-x^2 + 6x - 8) \, dx,## but other values of ##F(x)## must be given by something else. What would that be?
(C) is wrong; that is to say, the formula is wrong, but I have not checked the numerical answer.
(E) is partly right, but it looks partly wrong as well; it is hard to say, since what you wrote is almost incomprehensible.
 
  • #4
33,262
4,963
Thread moved to Calc & Beyond Homework section. Questions involving integrals do not belong in the Precalc section.
 

Related Threads for: Continuous Probability

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
2
Views
1K
Replies
3
Views
1K
Replies
5
Views
2K
  • Last Post
Replies
5
Views
3K
Replies
5
Views
4K
Replies
10
Views
887
Top