If $X$ is a random variable with cumulative distribution function $F(x)$ and its probability distribution is given by the following table:

$X = x$	$-1.5$	$-0.5$	$0.5$	$1.5$	$2.5$
$P(X = x)$	$0.05$	$0.2$	$0.15$	$0.25$	$0.35$

Then,find the value of $F(1.5) - F(-0.5)$.

In a game,a man wins $Rs. 100$ if he gets $5$ or $6$ on a throw of a fair die and loses $Rs. 50$ for getting any other number on the die. If he decides to throw the die either until he gets a five or a six or to a maximum of three throws,then his expected gain/loss (in rupees) is

$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ 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:

If $P(X = x) = 5r^x$, $x = 1, 2, 3, \dots$ is the probability mass function of a discrete random variable $X$, then $r = $

If the mean of a Poisson variate $X$ is $1$,then $\sum_{r=0}^{\infty}|r-1| P(X=r)=$