Continuous Probability

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

FactChecker
Gold Member
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.

Ray Vickson
Homework Helper
Dearly Missed

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.

Mark44
Mentor
Thread moved to Calc & Beyond Homework section. Questions involving integrals do not belong in the Precalc section.