Which of the following functions is not a probability density function $(p.d.f.)$ of a continuous random variable $X$?

$A$ person plays a game of tossing a coin thrice. For each head,he is given $Rs. 2$ by the organiser of the game and for each tail,he has to give $Rs. 1.50$ to the organiser. Let $X$ denote the amount gained or lost by the person. Show that $X$ is a random variable and exhibit it as a function on the sample space of the experiment.

In a game,a man wins $₹ 40$ if he gets $5$ or $6$ on a throw of a fair die and loses $₹ 20$ for getting any other number on the die. If he decides to throw the die either until he gets a $5$ or $6$ or to a maximum of $3$ throws,then his expected gain/loss (in rupees) is:

If $X$ is a random variable with the distribution given below:

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = x_i)$	$k$	$3k$	$3k$	$k$

Then the value of $k$ and its variance are respectively given by:

For the probability distribution given by

$x = x_{i}$	$0$	$1$	$2$
$P_{i}$	$\frac{25}{36}$	$\frac{5}{18}$	$\frac{1}{36}$

the standard deviation $(\sigma)$ is

If the p.m.f. of a random variable $X$ is given by $P(X=x) = \frac{\binom{5}{x}}{2^{5}}$ for $x = 0, 1, 2, \ldots, 5$ and $0$ otherwise,then which of the following is not true?