Question

Under the hypotheses H. and H, the random variable X has the following conditional distributions: x > 0 |H) x < 0 11/2 0 < x < 2 |) 0 otherwise (a) Asumming equal prior probabilities, P(H) = P(H1),

Answer 1

To calculate the equal prior probabilities, we can use the total probability rule. Since there are two hypotheses, H and H1, and we assume they have equal prior probabilities, we can assign a probability of 0.5 to each hypothesis:

P(H) = P(H1) = 0.5

Now, let's move on to the conditional distributions of the random variable X:

P(x > 0 | H) = 1/2
P(x < 0 | H) = 1/2

P(0 < x < 2 | H1) = 1
P(x > 2 | H1) = 0
P(x < 0 | H1) = 0

Since the conditional distribution for H1 is only defined within the range of 0 < x < 2, the probability of any other value of x is 0.