Consider the continuous mixture f_x(x) = integral_Theta h(theta) f_Y(x, theta)d
ID: 2084584 • Letter: C
Question
Consider the continuous mixture f_x(x) = integral_Theta h(theta) f_Y(x, theta)d theta for scalar x where theta = (m, sigma^2) and d theta = dm middot d sigma^2. Also, f_Y (x, theta) denotes a parametric pdf with a mean m and a variance sigma^2. (a) If f_X (x) should have the same form as f_Y(x, theta_1) but with mean m_x = 3 and variance sigma_x^2 = 4, give the function h(theta). (b) If f_X (x) should equal 3 f_Y(x, theta_1) + 7 f_Y(x, theta_2) with theta_1 = (2, 3) and theta_2 = (5, 9), give the function h(theta). (c) Considering your answers to parts (a) and (b), which mixture is more general, the parametric mixture or the continuous mixture?Explanation / Answer
the answer is option B CONTINUOS MIXTURE IS MORE .so this is the answer
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