Three fair coins with faces numbered 1 and 0 are tossed simultaneously. Then variance (X) of the probability distribution of random variable $$\mathrm{X}$$, where $$\mathrm{X}$$ is the sum of numbers on the upper most faces, is

The p.m.f of random variate $$\mathrm{X}$$ is $$P(X)= \begin{cases}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \ldots, \mathrm{n} \\ 0, & \text { otherwise }\end{cases}$$

Then $$\mathrm{E}(\mathrm{X})=$$

An experiment succeeds twice as often as it fails. Then the probability, that in the next 6 trials there will be atleast 4 successes, is

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks is