Question

Let X be a continuous random variable with probability density function

f ₓ (x)={ 3/4 x(2−x) for 0≤x≤2
0 o/w
Determine the distribution function Fₓ
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Answer 1

To find the cumulative distribution function Fₓ for the continuous random variable X with the given probability density function, integrate the function from 0 to x to calculate the probability that X is less than or equal to a value x within the range [0, 2].

Step-by-step explanation:

The student's question is about finding the cumulative distribution function (CDF), denoted FX(x), for a continuous random variable X with a given probability density function fX(x). The probability density function provided is fX(x) = 3/4 x(2 - x) for 0 ≤ x ≤ 2 and 0 otherwise. To determine the CDF FX(x), we integrate the probability density function from the lower bound of the variable's range up to the variable x.

The integration of fX(x) over the range from 0 to x (where 0 ≤ x ≤ 2) gives us the CDF FX(x), which is the probability that the variable X will take on a value less than or equal to x.