EXERCISE 11.5

. Compute P X k for the binomial distribution, B n p ( , ) where (i) n k (ii) n k (iii) n k . The probability that Mr.Q hits a target at any trial is . Suppose he tries at the target times.

Find the probability that he hits the target (i) exactly times (ii) at least one time. . Using binomial distribution find the mean and variance of X for the following experiments (i) A fair coin is tossed times, and X denote the number of heads. (ii) A fair die is tossed times, and X denote the number of times that four appeared.

. The probability that a certain kind of component will survive a electrical test is . Find the probability that exactly of the components tested survive. .

A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is % . The inspector of the retailer randomly picks items from a shipment. What is the probability that there will be (i) at least one defective item (ii) exactly two defective items?

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

The mean and standard deviation of a binomial variate X are respectively and . Find (i) the probability mass function (ii) P X