Question: [12 Marks]

True, False or Uncertain: Justify your answer

1. The population mean, \(\mu \), is used to estimate the sample mean, \(\bar{X}\) .
2. If P(A) = 0.4, P(B) = 0.5, and P(A \(\cap \) B) = 0.20, then the events A and B are mutually exclusive.
3. A jug contains 5 black marbles and 5 white marbles well mixed. A marble is removed and its color noted. A second marble is removed, without replacing the first marble, and its color is also noted. If x is the total number of black marbles in the two draws, then x has a binomial distribution.
4. The mean and variance of the Poisson distribution are equal.

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