The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:

$X$	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F(X)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Then,find $P[X=3]$.

$A$ random variable $X$ has the following distribution.

$X = x_{i}$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x_{i})$	$0.1$	$k$	$0.2$	$2k$	$3k$	$k$

Then the variance of this distribution is

$A$ bakerman sells $5$ types of cakes. Profit due to sale of each type of cake is respectively $Rs \ 2$,$Rs \ 2.5$,$Rs \ 3$,$Rs \ 1.5$ and $Rs \ 1$. The demands for these cakes are $20 \%$,$5 \%$,$10 \%$,$50 \%$ and $15 \%$ respectively. Then the expected profit per cake is:

The following table represents the probability distribution of a random variable $X$ for some $k \in Q$. Find the value of $k$.

$X=x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X=x)$	$0.1$	$k$	$0.2$	$2k$	$0.3$	$k$

For the following probability distribution,the standard deviation of the random variable $X$ is:

$X$	$2$	$3$	$4$
$P(X=x)$	$0.2$	$0.5$	$0.3$

$A$ biased coin with probability $p$ $(0 < p < 1)$ of getting a head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $\frac{2}{5}$, then $p=$