Question

Find the expected value of the random variable X and its variance having the following density function details explanation

                                   f(x) = 5 (1-x⁴)         0<x<2

                                         = 0                   elsewhere

Answer 1

Since $f\left( 1.5 \right) =5\left( 1-1.5^4 \right) =-20.3125<0$ , the function is not a density function, hence the expectation and variance cannot be calculated.