Let a pair of dice be thrown and the random variable $X$ be the sum of the numbers that appear on the two dice. Find the mean or expectation of $X$.

If a discrete random variable $X$ takes values $0, 1, 2, 3, \ldots$ with probability $P(X=x) = k(x+1) 5^{-x}$,where $k$ is a constant,then $P(X=0)$ is

If two dice are thrown and if $X$ denotes the sum of the numbers that show up on the faces of the dice, then the mean of the random variable $X$ is

Find the probability distribution of the number of successes in two tosses of a die,where a success is defined as 'six appears on at least one die'.

Find the mean number of heads in three tosses of a fair coin.

In a game,$3$ coins are tossed. $A$ person is paid ₹ $100$,if he gets all heads or all tails; and he is supposed to pay ₹ $40$,if he gets one head or two heads. The amount he can expect to win/lose on an average per game in (₹) is