If a random variable $X$ follows the Poisson distribution with variance $3$, then $P(X=r)$ is maximum, when $r=$

In a city,it is found that $10$ accidents took place in a span of $50$ days. Assuming that the number of accidents follows the Poisson distribution,the probability that there will be $3$ or more accidents in a day in that city is

If a random variable $x$ has the probability distribution as follows:

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(x)$	$0$	$2k$	$k$	$3k$	$2k^2$	$2k$	$k^2+k$	$7k^2$

Then $P(3 < x \leq 6)$ is equal to:

Let $X$ be a continuous random variable with the probability density function (p.d.f.) given by $f(x) = \begin{cases} kx, & 0 \leq x < 1 \\ k, & 1 \leq x < 2 \\ -kx + 3k, & 2 \leq x < 3 \\ 0, & \text{otherwise} \end{cases}$. Find $P(2 < X \leq 3)$.

India plays two matches each against Australia and West Indies. The probabilities of India scoring $0, 1,$ and $2$ points in a match are $0.45, 0.05,$ and $0.50$ respectively. Assuming the results are independent,what is the probability that India scores at least $7$ points?

$A$ bag contains $2$ white and $1$ red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If $X$ denotes the number of red balls recorded in the two draws,describe $X$.