SOLUTION: Let X be a random variable with probability density function given by:           | 0, if x <0 f (x) = { cx, if 0 <= x <= 2           | 0, if x> 2 a) Get the value of consta

Algebra.Com
Question 1105410: Let X be a random variable with probability density function given by:
          | 0, if x <0
f (x) = { cx, if 0 <= x <= 2
          | 0, if x> 2
a) Get the value of constant c.
b) Get the cumulative distribution function F (x).
c) Get P (1/4 < X <3/4).
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


a) Get the value of constant c.
Since f(2) = c(2) = 2c

f(x) has the graph:



Since this is a probability density function, the area between
the graph (in red) and the x-axis is 1.  Since the entire area 
is the area of the right triangle, we just use the formula for 
the area of a triangle:

 
So since the area A of the triangle is 1, 

 





And therefore



So the point (2,2c) is the point (2,1), 
and the graph of f(x) is

b) Get the cumulative distribution function F (x).

c) Get P (1/4 < X <3/4). 


Edwin
RELATED QUESTIONS

Let X be a continuous random variable. Can the function f(x) = 2^(-x) for x > 0 and 0... (answered by greenestamps)
Let X be a continuous random variable. Can the function {{{ f(x)=2^(-x) }}} for x > 0 and (answered by Edwin McCravy)
If the probability density function of a continuous random variable X is f(x)=0.5 x for... (answered by greenestamps)
Let X be a continuous random variable with density function f(x) = { theta*x +... (answered by math_tutor2020)
If X is continuous random variable with probability density function f(x) = {(ax,... (answered by parmen)
Let the probability density function of X be f(x) = {e−x if x > 0 } {0... (answered by ikleyn)
Excel RAND Function. Most computer languages include a function that can be used to... (answered by onyulee)
Let X be a random variable with cumulative distribution function F(x) = { 0 if x ≤ 0 } (answered by ikleyn)
Let the random variable X have the density function f(x)= {kx for... (answered by Greenfinch)