For a random variable $X$, it is given, $E\left(X\right)=5$ and $\mathrm{Var}\left(X\right)=16$. Find the positive values of $a$ and $b$ such that $Y=aX-b$ has expectation $0$ and variance $4$.

Determine the mean, variance and standard deviation of the following probability distribution.

Find the mean, variance and standard deviation of the number of heads in two tosses of a coin.

Find the mean and variance of the number of multiples of $3$ in two tosses of a die.

Two dice are drawn simultaneously. Suppose $X$ denotes the number of sixes. Find the expectation and variance of $X$.

Find the mean, variance and standard deviation of the number of heads in a simultaneous toss of three coins.

A coin is tossed $4$ times. Let $X$ denote the number of heads. Find the probability distribution of $X$.

A coin is tossed $4$ times. Let $X$ denote the number of heads. Find the mean and variance of $X$.