7. (10 pts) Assume that a discrete random variable X can take one of the values

Question

7. (10 pts) Assume that a discrete random variable X can take one of the values of 0 to 6, and the probability of each value can be different depending on the distributions that X follows. For the distributions we are considering, denoted as Distn 1 and Distn 2, the probabilities are given in the following table. 0.1 0.1 Distn 1 0.1 0.1 0.1 0.2 0.3 Distn 2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 Given one observed value of X, we want to test what the distribution of X is. The null and alternative hypothesis are stated in the following. Ho: X follows Distn 1 H1: A follows Distn 2 VS

Explanation / Answer

Rejection region {x=6}

the probability of type II error = P(Accepting H0 when it is false) = 1- P(Rejecting H0 when it is false)

= 1- P(X=6 | X is drawn from distribution 2 )

=1- 0.1

= 0.9

So,

Probability of type II error = 0.9

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