Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such that each color appears only two times on the die. If the die is thrown thrice, the probability of obtaining red colour on top face of the die at least twice is ________.

A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3}$$ and $${1 \over 6}$$, respectively. Then mean value and the variance of the number of defective pieces produced by

In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard deviation of $$x$$ is