Given below is the distribution of a random variable $X$:

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$\lambda$	$2\lambda$	$3\lambda$	$4\lambda$

If $\alpha=P(X < 3)$ and $\beta=P(X>2)$,then $\alpha: \beta=$

$A$ service station manager sells gas at an average of ₹ $100$ per hour on a rainy day,₹ $150$ per hour on a dubious day,₹ $250$ per hour on a fair day,and ₹ $300$ per hour on a clear sky day. If weather bureau statistics show the probabilities of weather as follows,then his mathematical expectation is:

Weather	Clear	Fair	Dubious	Rainy
Probability	$0.50$	$0.30$	$0.15$	$0.05$

$A$ random variable $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3)=2 P(X=1)$ and $P(X=2)=0.3$,then $P(X=0)$ is

Two dice are rolled. If a random variable $X$ denotes the sum of the numbers on them and $\mu$ denotes the mean of $X$, then $\mu+P(X < 5)+P(X>9)+P(X=7)=$

Let $X$ be a random variable representing the number of heads obtained when three fair coins are tossed simultaneously. Find the value of $P(X = 2)$.

$A$ random variable $X$ assumes values $1, 2, 3, \ldots, n$ with equal probabilities. If $\operatorname{var}(X) : E(X) = 4 : 1$,then $n$ is equal to