Please show all your workings and answers clearly.

2. Two indistinguishable unfair coins are tossed in such a way that it cannot be determined which coin is which. Each coin has been weighted so that it comes up heads with probability 0.6 and tails with probability 0.4. (a) Give the sample space for the experiment of tossing the two coins at the same time. Your sample space should contain 3 outcomes. (b) In one or two sentences, explain why three outcomes are suicient for your sample space. (c) A random variable X maps the sample space to the set {0, 1, 2} where each outcome maps to the number of heads in the outcome. Find the probability density/ mass function (or p.d.f.) fX and the cumulative distribution function (or c.d.f.) F X for the random variable X. (d) Calculate the expectation E(X2)