If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights
(i) exactly 10 will have a useful life of at least 600 hours;
(ii) at least 11 will have a useful life of at I least 600 hours;  
(iii) at least 2 will not have a useful life of at : least 600 hours.

If the sum of mean and variance of a binomial distribution is 4.8 for 5 trails, find the distribution.

The difference between the mean and the variance of a binomial distribution is 1 and the difference between their squares is 11. Find n.

The mean of a binomial distribution is 6 and its standard deviation is 3. Is this statement true or false?

The probability of success of an event is p and that of failure is q. Find the expected number of trails to get a first success.

If \(\mathrm{F}(\mathrm{x})=\frac{1}{\pi}\left(\frac{\pi}{2}+\tan ^{-1} x\right),-\infty<\mathrm{x}<\infty\) is a distribution function of a continuos variable x, find \(\mathrm{P}(0 \leq \mathrm{x} \leq 1)\)