1. Which of the following statement is INCORRECT? O If X1, . ..;Xn is a random sample from a normal distribution with population mean 0 and variance 1, then Vix S must follow a t distribution, where X denotes the sample mean and S denotes the sample standard deviation. O If X1, ...;Xn is a random sample from a normal population with population mean 1 and variance 2, then 0.5 ((X1 - 1)' + (X2 - 1)' + ... + (X, - 1)?) follows a chi-square distribution with degrees of freedom n. O If Y1 and Y's follow chis-square distributions with degrees of freedom m, and ng respectively, then na Yi/ (m )2) must follow an F distribution. O If T follows a t distribution with degrees of freedom n, then 7 must follow an F distribution.6. Which of the following random variable can be model with a binomial distribution? The number of tagged fish out of 20 fish that a fisherman randomly catches with replacement from a pond of 50 fish. It is known that 20% of the fish have been tagged. The number of tagged fish If a fisherman randomly catches 20 fish without replacement from a pond of 50 fish. It is known that 20%% of the fish have been tagged. The number of tagged fish if a fisherman randomly catches 20 fish without replacement from a pond of many fish. It is known that 20% of the fish have been tagged. The number of fish a fisherman has to catch randomly with replacement so that 20 fish that have been tagged are caught from a pond of many fish. It is known that 20% of the fish have been tagged