Determine the binomial distribution whose mean is $9$ and variance is $6$?

Find the binomial distribution whose mean is $5$ and variance is $2.5$.

The mean and variance of a binomial distribution are $4$ and $\left(\frac{4}{3}\right)$ respectively. Find $\mathrm{P}(\mathrm{X}\ge 1)$.

For a binomial distribution, the mean is $6$ and the standard deviation is $\sqrt{2}$. If the probability of getting $5$ successes is ${}^{9}C_5\frac{k}{3^9}$, then find the value of $k$.

In a binomial distribution, the sum and the product of the mean and the variance are $\left(\frac{25}{3}\right)$ and $\left(\frac{50}{3}\right)$respectively. Find the distribution.

Obtain the binomial distribution whose mean is $10$ and standard deviation is $2\sqrt{2}$.

Bring out the fallacy, if any, in the following statement:

‘The mean of a binomial distribution is $6$ and its variance is $9’$