In a game, 3 coins are tossed. A person is paid ₹ 7 /-, if he gets all heads or all tails; and he is supposed to pay ₹ 3 /-, if he gets one head or two heads. The amount he can expect to win on an average per game is ₹

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of sixes in two tosses, then the probability distribution of $$\mathrm{X}$$ is given by

For a binomial variate $$\mathrm{X}$$ with $$\mathrm{n}=6$$ if $$P(X=4)=\frac{135}{2^{12}}$$, then its variance is

The p.d.f. of a discrete random variable is defined as $$\mathrm{f}(x)=\left\{\begin{array}{l} \mathrm{k} x^2, 0 \leq x \leq 6 \\ 0, \text { otherwise } \end{array}\right.$$

Then the value of $$F(4)$$ (c.d.f) is