A die is thrown 9000 times and the outcome of 3 or 4 is observed 3240 times.

1. A die is thrown 9000 times and the outcome of 3 or 4 is observed 3240 times. Show

that the die cannot be regarded as an unbiased one and find the limits between which

the probability of a throw of 3 or 4 lies.

2. Find the maximum likelihood estimator for the parameter l of a Poisson distribution

on the basis of a sample of size n . Also find its variance.

3.In a binomial distribution consisting of 5 independent trials, probabilities of 1 and 2successes are 0.4096 and 0.2048 respectively. Find the parameter ' p ' of thedistribution.