6. Find the cumulative distribution function and the density (if it exists) of a random variable...

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6. Find the cumulative distribution function and the density (if it exists) of a random variable X defined on N = = [0, 1] by X(w) = −2 × ¹[0,‡](w) + 3 × 1(4,1](w). 7. Find the cumulative distribution function and the density (if it exists) of a random variable X defined on 2 = [0, 1]. Use this density to find the expectation and the variance of X. a) X(w) = w-1/, b) X(w) = 2w². 6. Find the cumulative distribution function and the density (if it exists) of a random variable X defined on N = = [0, 1] by X(w) = −2 × ¹[0,‡](w) + 3 × 1(4,1](w). 7. Find the cumulative distribution function and the density (if it exists) of a random variable X defined on 2 = [0, 1]. Use this density to find the expectation and the variance of X. a) X(w) = w-1/, b) X(w) = 2w².