Let X have probability density function fX(x) = 1/4 0 < x < 1 3/8 3 < x < 5 0 otherwise. (a) Find the cumulative distribution function of X. (b) Let Y = 1/X. Find the probability density function fY (y) for Y . Hint: Consider three cases: 1 5 ≤ y ≤ 1 3 , 1 3 ≤ y ≤ 1, and y ≥ 1.
Added by Victor Manuel W.
Step 1
- For x ≤ 0: F_X(x) = 0. - For 0 < x < 1: F_X(x) = ∫_0^x (1/4) dt = x/4. - For 1 ≤ x ≤ 3: F_X(x) = ∫_0^1 (1/4) dt = 1/4. - For 3 < x < 5: F_X(x) = ∫_0^1 (1/4) dt + ∫_3^x (3/8) dt = 1/4 + (x-3)/ (8/3) = 1/4 + (3/8)(x-3). - For x ≥ 5: F_X(x) = 1. So, in piecewise Show more…
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