Problem Set 05: Solution Key

Archives and Selection Effects

Worked Solutions

1. Parallax quality cut

Ratio = 3.4/0.9 = 3.78, which is below 5, so this source fails the quality cut.

CriterionPoints
Correct ratio8
Correct pass/fail7

2. Distance from parallax

d = 1000/6.2 = 161.3 pc.

CriterionPoints
Correct formula5
Correct value10

3. Magnitude cut

G = 13.2 < 14 passes; G = 15.8 > 14 fails.

CriterionPoints
Correct classification of both15

4. Combined sample

Parallax/error: S1=20.7 (pass), S2=3.8 (fail), S3=45.5 (pass), S4=13.3 (pass), S5=2.5 (fail). Magnitude cut (G<14): S1 pass, S2 pass, S3 fail (15.5), S4 pass, S5 pass. Sources passing BOTH cuts: S1, S4.

CriterionPoints
Correct parallax pass/fail for all five8
Correct final retained sample7

Grading Notes

Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Common partial-credit errors: omitting units, failing to combine uncertainties in quadrature, or overstating the confidence of a marginal (SNR 3–5) result.