If a random variable $X$ denotes the number that appears on the upper face of a die when it is rolled,then $\frac{\text{Variance of } X}{\text{Mean of } X}$ is equal to

Let $X$ be a random variable with probability distribution function,$P(X=x)=K\left(\frac{2}{5}\right)^x, x=1, 2, 3, \ldots$. Then,the value of $K$ is

$A$ student studies for $X$ number of hours during a randomly selected school day. The probability distribution of $X$ is given by the following form,where $k$ is a constant:
$P(X=x) = \begin{cases} 0.2, & \text{if } x=0 \\ kx, & \text{if } x=1 \text{ or } 2 \\ k(6-x), & \text{if } x=3 \text{ or } 4 \\ 0, & \text{otherwise} \end{cases}$
The probability that the student studies for at most two hours is:

Two numbers are selected at random,without replacement from the first $6$ positive integers. Let $X$ denote the larger of the two numbers. Then $E(X) = $

$A$ coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails,then $P(X=1) = $

Bismuth has a half-life of $5$ days. If a sample originally has a mass of $800 \text{ mg}$, then the mass remaining after $30$ days will be: (in $\text{ mg}$)