$A$ coin is tossed twice in succession. Let $X$ represent the number of tails in two tosses,then the probability distribution of $X$ is given by

Let $X$ be a random variable,and let $P(X=x)$ denote the probability that $X$ takes the value $x$. Suppose that the points $(x, P(X=x))$ for $x=0,1,2,3,4$ lie on a fixed straight line in the $xy$-plane,and $P(X=x)=0$ for all $x \in \mathbb{R} \setminus \{0,1,2,3,4\}$. If the mean of $X$ is $\frac{5}{2}$,and the variance of $X$ is $\alpha$,then the value of $24\alpha$ is:

For a Poisson variate $X$,if $P(X=2)=3 P(X=3)$,then the mean of $X$ is:

In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random. We take $X=0$ if he opposes the proposal and $X=1$ if the member is in favour. Then the variance of $X$ is:

Two dice are thrown simultaneously. If $X$ denotes the number of sixes,find the expectation of $X$.

If the probability that an individual will suffer a reaction from an injection of a drug is $0.001$,then the probability that out of $2000$ individuals having that injection,more than $2$ individuals will suffer a reaction,is