3. (15%) Let X1, X2 be a random sample of size n = 2 from a distribution with p.d.f. f(x) = 4x^3, 0 < x < 1, zero elsewhere. Given the ratio Y = X1 / X2, find (1)(10%) E(Y). (Round the answer to 4 decimal places)

4. (10%) A die was cast $n = 120$ independent times and the following data resulted: | Spots up | 1 | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | --- | | Frequency | b | 20 | 20 | 20 | 20 | 40-b | If we use a chi-square test, for what values of b would the hypothesis that the die is unbiased be rejected at the 0.025 significance level? $$(\chi^2{(5),\alpha=0.025} = 12.8; \chi^2{(6),\alpha=0.025} = 14.4; \chi^2{(5),\alpha=0.05} = 11.1; \chi^2{(6),\alpha=0.05} = 12.6)$$

3. (15%) Let \( X{1}, X{2} \) be a random sample of size \( n = 2 \) from a distribution with p.d.f. \( f(x) = 4x^{3} \), \( 0 < x < 1 \), zero elsewhere. Given the ratio \( Y = X{1} / X{2} \), find

(1)(10%) E(Y). (Round the answer to 4 decimal places)

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3. (15%) Let \( X{1}, X{2} \) be a random sample of size \( n = 2 \) from a distribution with p.d.f. \( f(x) = 4x^{3} \), \( 0 < x < 1 \), zero elsewhere. Given the ratio \( Y = X{1} / X{2} \), find (1)(10%) E(Y). (Round the answer to 4 decimal places)

相關申論題

相關試卷

3. (15%) Let \( X{1}, X{2} \) be a random sample of size \( n = 2 \) from a distribution with p.d.f. \( f(x) = 4x^{3} \), \( 0 < x < 1 \), zero elsewhere. Given the ratio \( Y = X{1} / X{2} \), find

(1)(10%) E(Y). (Round the answer to 4 decimal places)