Given the probability density function (p.d.f.) of the random variable X, $f(x) = \dfrac{1}{2a}$, $0 < x < 2a$, $a > 0$
$= 0$, otherwise, then which of the following is correct ?

Consider a game of tossing a six sided fair die. If the face that comes up is $6$, the player wins Rs. $36$ and he loses Rs. $k^2$, where $k$ is the face that comes up $k = \{1, 2, 3, 4, 5\}$, then the expected winning amount in this game in Rs. is...

A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is $\ldots$

If the p. d. f. of a continuous random variable X is given by $f(x) = \begin{cases} k(9 + 8x - x^2), & \text{for } -1 \leq x \leq 4 \\ 0, & \text{otherwise} \end{cases}$ then the value of $k$ is $\ldots$