# probability density function

• Dec 5th 2009, 04:18 AM
compufatwa
probability density function
suppose that X is a continuous random variable with probability density function given by

f(X) = x^2 + (2/3)x +(1/3) for <or = x <or = c

(a) what must be the value of c
assuming this value of c , do the following :-

b) plot f(x)
c) compute and plot F(x)
d)compute p(1/3 <or = X < or = 2/3 ) , E(X) , var (X)
• Dec 5th 2009, 02:28 PM
mr fantastic
Quote:

Originally Posted by compufatwa
suppose that X is a continuous random variable with probability density function given by

f(X) = x^2 + (2/3)x +(1/3) for <or = x <or = c

(a) what must be the value of c
assuming this value of c , do the following :-

b) plot f(x)
c) compute and plot F(x)
d)compute p(1/3 <or = X < or = 2/3 ) , E(X) , var (X)

Use $\displaystyle \int_{0}^{c} f(x) \, dx = 1$ and solve for c.

Then check that $\displaystyle f(x) \geq 0$ over the interval $\displaystyle 0 \leq x \leq c$ for the value of c that you find.
• Dec 5th 2009, 02:35 PM
mr fantastic