$7$ coins are tossed simultaneously and the number of heads turned up is denoted by the random variable $X$. If $\mu$ is the mean and $\sigma^2$ is the variance of $X$,then $\frac{\mu \sigma^2}{P(X=3)}=$

Tom and Jerry play a game of alternately throwing an unfair coin. The first one to get a head wins. If Tom starts the game,he has a $62.5 \%$ chance of winning. Suppose this coin is tossed $5$ times,then the probability of getting exactly $3$ heads is

The probability that a missile hits a target successfully is $0.75$. In order to destroy the target completely,at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is $NOT$ less than $0.95$,is. . . . .

For an initial screening of an admission test,a candidate is given $50$ problems to solve. If the probability that the candidate can solve any problem is $\frac{4}{5}$,then the probability that he is unable to solve less than two problems is

If the standard deviation of the random variable $X$ is $\sqrt{3pq}$ and the mean is $3p$,then $E(X^2) = . . . . . . .$

$A$ random variable $X$ follows a binomial distribution in which the difference between its mean and variance is $1$. If $2 P(X=2)=3 P(X=1)$,then $n^2 P(X>1)=$