$A$ random variable $X$ has the following probability distribution:

$X$	$1, 2, 3, 4, 5$
$P(X)$	$K^2, 2K, K, 2K, 5K^2$

Then $P(X > 2)$ is equal to:

$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a spade card. The probability that he will fail the first two times is:

For the following probability distribution,find the expected value of $X$:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$P(x)$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

If the probability function of a random variable $X$ is given by $P(X=k) = \frac{3^{ck}}{k!}$ for $k = 1, 2, 3, \ldots$ (where $c$ is a constant),then $c =$

$A$ random variable $X$ has its range $\{-1, 0, 1\}$. If its mean is $0.2$ and $P(X=0)=0.2$,then $P(X=1)=$

Let $X$ denote the number of hours you study on a Sunday. It is known that $P(X=x) = \begin{cases} 0.1 & \text{if } x=0 \\ kx & \text{if } x=1, 2 \\ k(5-x) & \text{if } x=3, 4 \\ 0 & \text{otherwise} \end{cases}$ where $k$ is a constant. Then the probability that you study at least two hours on a Sunday is