一、(15%) If the moment-generating function of X is M(t) = (2/5)e^t + (1/5)e^2t + (2/5)e^3t, find the mean, variance, probability density function of X.

五、(25%) To test two method of instruction, 50 students are selected at random for each of two groups. At the end of the instruction period each student is assigned a grade (A, B, C, D, or F) by an evaluating team. The data are recorded as follows: | | Grade | | | | | | | --- | --- | --- | --- | --- | --- | --- | | | A | B | C | D | F | Total | | Group I | 8 | 13 | 16 | 10 | 3 | 50 | | Group II | 4 | 9 | 14 | 16 | 7 | 50 | Please use a chi-square test with α = 0.05 to test the equality of the distributions of grade. The critical value of chi-square distribution for above test is as follows: | r | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | | χ²₀.₀₅(r) | 5.991 | 7.815 | 9.488 | 11.070 | 12.590 | | χ²₀.₀₂₅(r) | 7.378 | 9.348 | 11.140 | 12.830 | 14.450 | | * P(≥χ²ₐ(r)) = α for X ~ χ²(r). | | | | | |

一、(15%) If the moment-generating function of X is

$$M(t) = (2/5)e^t + (1/5)e^{2t} + (2/5)e^{3t},$$

find the mean, variance, probability density function of X.

相關申論題

相關試卷

一、(15%) If the moment-generating function of X is $$M(t) = (2/5)e^t + (1/5)e^{2t} + (2/5)e^{3t},$$ find the mean, variance, probability density function of X.

相關申論題

相關試卷

一、(15%) If the moment-generating function of X is

$$M(t) = (2/5)e^t + (1/5)e^{2t} + (2/5)e^{3t},$$

find the mean, variance, probability density function of X.