Parthasarathi Mukhopadhyay and Manabendra Nath Mukherjee Solutions for Exercise 6: EXERCISE

In a  Bernoulli sequence of $5$ trials if the probability of getting $3$ successes is six times that of getting $2$ successes, then the mean of its binomial distribution is $\frac{30}{7}$.

For a binomial distribution, the mean and standard deviation are respectively $6$ and $\sqrt{5}$. The probability of getting a non-zero value from this distribution is $1-{\left(\frac{5}{6}\right)}^m$, then find the value of $m$.

The probability that a fruit is stale is $0.2$. Find the mean and variance for the distribution of stale fruit in a total of $800$ fruits.

If two dice are rolled $12$ times, obtain the mean and the variance of the distribution of successes, if getting a total greater than $4$ is considered a success.

If one out of $10$ persons are illiterate, find the mean and standard deviation of the number of literate persons out of a total of $500$ persons.

For a binomial variate $X$, the events $(X=49)$ and $(X=50)$ are most probable. If the mean of $X$ is $49.6$, find the variance of $X$ and hence find the binomial distribution of the variate $X$.

If the sum of the mean and variance of a binomial distribution for $5$ trails is $1.8$, find the distribution.

The sum and product of the mean and variance of a binomial distribution are respectively $10$ and $24$. Find the distribution.