Find the binomial probability distribution whose mean is $3$ and variance is $2$.

Consider $5$ independent Bernoulli trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$,then $p$ lies in the interval:

Four fair dice are thrown independently $27$ times. Then the expected number of times,at least two dice show up a three or a five,is

The mean and variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of exactly two successes is

If the mean and the variance of a binomial variate $X$ are $1$ and $0.75$ respectively, then which of the following is true?

If $\mu$ and $\sigma^{2}$ are the mean and variance of a random variable $X$ whose probability mass function is given by $P(X=x) = \binom{6}{x} \left(\frac{1}{3}\right)^{x} \left(\frac{2}{3}\right)^{6-x}$ for $x = 0, 1, 2, \ldots, 6$,then the value of $2\mu + 12\sigma^{2}$ is: