How Do You Solve These Continuous Probability Problems?

[noreturn2]

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]

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 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]

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