For the following probability distribution, the standard deviation of the random variable $X$ is:
$X: 0, 1, 2$
$P(X): 0.3, 0.4, 0.3$

$A$ 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:

If a random variable $X$ follows a Poisson distribution such that $P(X=1) = 3P(X=2)$, then $P(X=3) =$

Two bad eggs are mixed accidentally with $10$ good ones. If three eggs are drawn at random from this lot in succession without replacement, then the variance of the probability distribution of the number of bad eggs drawn is

$A$ person throws an unbiased die. If the number shown is even,he gains an amount equal to the number shown. If the number is odd,he loses an amount equal to the number shown. Then his expectation is ₹.

Two coins are tossed simultaneously. Then,the value of $E(X)$,where $X$ denotes the number of heads is