Respected Tutor, please help me to solve following question, as I am stuck in it, can you please please help to solve and explain following sum???

Let the probability space (, F, P), where = {1, 2, 3}, F = 2(2 raise to Omega), and P satisfies P({1}) = 0.5 and P({2}) = 0.1. Consider the random variable X : R defined by X() = 2+3.

a) Find X1 ([1, 5)) and X1 ([2, 4] {7}).

b) Derive the probability distribution of X as the induced measure PX1(X raise to -1) . Be sure to define it for any Borel set B B.

(c) What is the support of X?

(d) Derive the cumulative distribution function (cdf) of X. Be sure to define it for any x R.

(e) Is X discrete or continuous? Justify.