In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.

The probability distribution of a random variable $X$ is given by

$X=x_i$	$0$	$1$	$2$	$3$	$4$
$P(X=x_i)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

Then the variance of $X$ is

If a Poisson variate $X$ satisfies $P(X=2) = P(X=3)$, then $P(X=5) =$

$A$ random variable $X$ has the following probability distribution:
| $x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
|---|---|---|---|---|---|---|---|---|
| $P(x)$ | $0.15$ | $0.23$ | $0.12$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
For the events $E = \{x \text{ is a prime number}\}$ and $F = \{x < 4\}$,the probability $P(E \cup F)$ is:

If the mean of a Poisson distribution is $\frac{1}{3}$,then the ratio $P(X=1) : P(X=2)$ is

$A$ random variable $X$ has the following probability distribution:

$X$	$0$	$1$	$2$
$P(X)$	$\frac{25}{36}$	$k$	$\frac{1}{36}$

If the mean of the random variable $X$ is $\frac{1}{3}$,then the variance is: