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Unformatted text preview: to choose H2 ), and suppose the cost Cij for deciding Hi when
arej equally as following0 = P1 = P2 = 1/3. Determine the
H is true are likely, P Assume all three hypotheses
optimal decision rule for
choosing between H0 and H1 in order to minimize the expected cost. Simplify the rule as much as possible.
C00 = C11 = 0
C01 = C10 = 1
C02 = 1, C12 = 2 Assume that all three hypothesis are equally probable, i.e., P0 = P1 = P2 = 1/3.
Determine the optimal decision rule for choosing between H0 and H1 in order
to minimize the expected cost. Simplify the rule as much as possible.
(d) Compare your decision rule in part (a) and part (c). Intuitively explain what
is the eﬀect of having the extra hypothesis H2 . 3 3. Suppose that h, x, v are mutually independent random variables with
x ∼ N (3, 4), v ∼ N (0, 4) and where h takes on only two possible values, 1 and 3 with
P r(h = 1) = P r(h = 3) = 1/2.
Let
z = hx + v
(a) Determine the MMSE estimator of x given z and h (i.e. xM M SE ).
ˆ
(b) Determine the MMSE achieved by the above estimator. 4 4. Suppose a...
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This note was uploaded on 01/08/2013 for the course ECE 531 taught by Professor Natasha during the Spring '10 term at Ill. Chicago.
 Spring '10
 Natasha

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