# Thread: a continuous random variable with probability density function

1. ## a continuous random variable with 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)

2. Is the interval (0,c)?
Note that for continuous random variables
you can use (0,c) as well as [0,c]

Just integrate and set the probability equal to 1, to find c.

3. intergration from 0 to c x^2 + (2/3)x + 1/3

c
x^3 / 3 + x^2 /3 + x/3 |
0

c^3/ 3 + c^2 / 3 + c /3 =1 multiple by 3

c^3 + c^2 + c = 3

c =1

4. and for part b) plot f(x)

do i to choose random number an substitute at the integrated equation ?

5. divide by c-1 into your cubic, to find the other two roots
most likely c=1 is the only real root.

6. Originally Posted by compufatwa
and for part b) plot f(x)

do i to choose random number an substitute at the integrated equation ?

plot x vs f(x),

and $F(x)=\int_0^x f(t)dt$ for all x in (0,c)
F=0 if x<c
F=1 if x>c.

7. integration from 0 to x x^2 + 2/3 x + 1/3
x
[x^3 / 3 + 1/3 x^2 + 1/3 x |
0
x^4 /3 + 1/3 x^3 + 1/3 x^2 - 0

i do n't know if that what u mean u not

8. i think i have to take the equation that i have already integrated it and integrate iy a gain with interval 0 to x