A random variable has probability density function f(x) = 30 $x ^ { 2 }$ (1 - x $)^2$
(0 ≤ x ≤ 1). Compute its cumulative distribution F(x).
A) 10 $x ^ { 3 }$ - $15 x ^ { 4 }$ + 6 $x ^ { 5 }$ + 1
B) 10 $x ^ { 3 }$ - 15 $x ^ { 4 }$ + 6 $x ^ { 5 }$
C) 30x(1 - x)
D) 30 $x ^ { 2 }$ - 60 $x ^ { 3 }$ + $30 x ^ { 4 }$
E) none of these

Question

A random variable has probability density function f(x) = 30 $x ^ { 2 }$ (1 - x $)^2$ 
(0 ≤ x ≤ 1). Compute its cumulative distribution F(x).
A) 10 $x ^ { 3 }$ - $15 x ^ { 4 }$ + 6 $x ^ { 5 }$ + 1
B) 10 $x ^ { 3 }$ - 15 $x ^ { 4 }$ + 6 $x ^ { 5 }$
C) 30x(1 - x)
D) 30 $x ^ { 2 }$ - 60 $x ^ { 3 }$ + $30 x ^ { 4 }$
E) none of these

Quizplus · Accepted Answer

The cumulative distribution function F(x) is the integral of the probability density function f(x) from 0 to x. Integrating f(x) = 30 $x ^ { 2 }$ (1 - x $)^2$ over this interval gives F(x) = 10 $x ^ { 3 }$ - 15 $x ^ { 4 }$ + 6 $x ^ { 5 }$.

A Random Variable Has Probability Density Function F(x) = 30 x2x ^ { 2 }x2

A Random Variable Has Probability Density Function F(x) = 30 $x ^ { 2 }$