Answer:

Step-by-step explanation:
From the given data, the cumulative distribution function of a random variable can be represented as:

The objective is to estimate E(X), to do that, let's first evaluate the probability density function by differentiating the cumulative distribution function from above.

∴

The expected value of x i
.e E(X) can now be estimated by taking the integral:



![E(X) = \dfrac{1}{2}[\dfrac{x^2}{2}]^2_1](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5B%5Cdfrac%7Bx%5E2%7D%7B2%7D%5D%5E2_1)
![E(X) = \dfrac{1}{2}[\dfrac{4}{2}-\dfrac{1}{2}]](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5B%5Cdfrac%7B4%7D%7B2%7D-%5Cdfrac%7B1%7D%7B2%7D%5D)
![E(X) = \dfrac{1}{2} \times [\dfrac{3}{2}]](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5B%5Cdfrac%7B3%7D%7B2%7D%5D)
