help! Probability statistics

[匿名]

2011-10-10 12:15 am

probability statistics question:

1. A certain college gives aptitude tests in the sciences and the humanities to all entering freshmen. If X and Y are, respectively, the proportions of correct answers a student gets on the tests in the two subjects, the joint probability distribution of these random variables can be approximated with the joint probability density.

f(x,y)=2/5 * (2 x+ 3 y) for 0 < x < 1, 0 < y < 1
f(x,y)=0 elsewhere

What are the probabilities that a student will get
(a) Less than 0.40 on both tests; (b) More than 0.80 on the science test and less than 0.50 on the humanities test?

回答 (1)

用戶25975

2011-10-10 1:15 am

✔ 最佳答案

a) (2/5) ∫ (x = 0 → 0.4) ∫ (y = 0 → 0.4) (2x + 3y) dy dx

= (2/5) ∫ (x = 0 → 0.4) [2xy + 3y2/2] (y = 0 → 0.4) dx

= (2/5) ∫ (x = 0 → 0.4) (0.8x + 0.24) dx

= (2/5) [0.4x2 + 0.24x] (x = 0 → 0.4)

= 0.064

b) (2/5) ∫ (x = 0.8 → 1) ∫ (y = 0 → 0.5) (2x + 3y) dy dx

= (2/5) ∫ (x = 0.8 → 1) [2xy + 3y2/2] (y = 0 → 0.5) dx

= (2/5) ∫ (x = 0.8 → 1) (x + 0.375) dx

= (2/5) [x2/2 + 0.375x] (x = 0.8 → 1)

= 0.102

參考: 原創答案

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