119. 將某額定為 220 伏特、1000 瓦特之電熱器，以 110 伏特的電源供電，若要產生 75000 焦耳熱量，需供電多少分鐘？ 初等考 114
(A)2.5
(B)5
(C)7.5
(D)10

7 將某額定為 220 伏特、1000 瓦特之電熱器，以 110 伏特的電源供電，若要產生 75000 焦耳熱量，需供電多少分鐘？ (A) 2.5 (B)5 (C) 7.5 (D) 10

1. A person buys a new toothbrush every quarter. Only two colors are available: blue and pink. If the person uses a blue toothbrush in a given quarter, the probabilities of buying a blue or pink toothbrush in the next quarter are 0.3 and 0.7, respectively. If the person uses a pink toothbrush in a given quarter, the probabilities of buying a blue or pink toothbrush in the next quarter are 0.5 and 0.5, respectively. Suppose the person buys a blue toothbrush in quarter 1. Given that the person buys a pink toothbrush in quarter 4, the probability that the toothbrush colors in quarters 2 and 3 are the same lies in which of the following ranges?(A) Between 0.35 and 0.39(B) Between 0.40 and 0.44(C) Between 0.45 and 0.49(D) Between 0.50 and 0.54

2. Suppose a random variable has a right-skewed (positively skewed) distribution. Which of the following is correct?(A) Mean \( < \) Median \( < \) Mode(B) Mean \( < \) Mode \( < \) Median(C) Median \( < \) Mode \( < \) Mean(D) Mode \( < \) Median \( < \) Mean

3. Let X and Y be random variables with the following joint probability density function. \( f(X, Y) = e^{-X} \), \( 0 < Y < X \) First derive \( E(Y | X) \), and then evaluate it at \( X = 2 \). What is the resulting expected value? (A) \( \frac{1}{2} \) (B) 1 (C) 2 (D) None of the above

4. A random variable X has the following probability density function \( f(X) = \frac{e^{-X}}{(1+e^{-X})^2} \), \( -\infty < X < \infty \) Let \( Y = (1 + e^{-X})^{-1} \). Which of the following distributions does the probability density function of Y, f(Y), belong to? (A) Uniform distribution (B) Normal distribution (C) Exponential distribution (D) Poisson distribution

5. Suppose x1, x2, ..., xn is a random sample from a normal distribution with mean μ and variance σ², where both μ and σ² are unknown. Assume x1 = 2, x2 = 4, x3 = 4, x4 = 6, x5 = 8, x6 = 8, and x7 = 10. What is the 90% confidence interval for σ²? Hint: χ²₀.₀₅.₆ = 1.635, χ²₀.₀₅.₇ = 2.167, χ²₀.₉₅.₆ = 12.592, and χ²₀.₉₅.₇ = 14.067.(A) (3.81, 29.36)(B) (4.45, 34.25)(C) (3.41, 22.15)(D) (3.98, 25.84)

6. Consider the hypothesis test for a normal distribution with mean μ at significance level α: H0: μ = μ0 versus H1: μ ≠ μ0. Which of the following is correct?(A) \( \Pr \) (critical region \( |\mathrm{H}_0\rangle = 1 - \alpha \)(B) \( \Pr \) (critical region \( |\mathrm{H}_1\rangle = \Pr \) (type II error)(C) \( \Pr \) (reject \( \mathrm{H}0\mid \mathrm{H}0 \) ) \( = \) p-value(D) \( \Pr \) (reject \( \mathrm{H}0\mid \mathrm{H}1 \) ) \( = \) power

7. Suppose \( x_1, x_2, \dots, x_n \) is a random sample of size n from the following double exponential distribution \( f(x | \beta) = \frac{1}{2\beta} e^{-\frac{|x|}{\beta}} \). Assume that \( x_1 = -3, x_2 = 2, x_3 = 4, x_4 = -1 \), and \( x_5 = 1 \). First derive the maximum likelihood estimator of \( \beta \), and then evaluate it at the given sample values. What is the resulting estimate? (A) 0.6 (B) 1.67 (C) 2.2 (D) 0.45

8. Suppose $x1, x2, \ldots, xn$ is a random sample of size $n$ from a Poisson distribution with mean $\lambda$, and assume $n = 2k$ for some integer $k$. Consider the following estimator. $\hat{\lambda} = \frac{1}{2k} \sum{i=1}^{k} (x{2i} - x{2i-1})^2$ Which of the following is correct?(A) \( \hat{\lambda} \) is a linear and an unbiased estimator.(B) \( \hat{\lambda} \) is a linear but biased estimator.(C) \( \hat{\lambda} \) is not a linear but an unbiased estimator.(D) \( \hat{\lambda} \) is neither a linear nor an unbiased estimator.

9. Suppose $x1, x2, \ldots, x_n$ is a random sample of size $n$ from a normal distribution with mean $\mu$ and variance $\sigma^2$. What is the Cramér-Rao lower bound for $\sigma^2$?(A) $\frac{\sigma^2}{n}$(B) $\frac{\sigma^2}{n-1}$(C) $\frac{2\sigma^4}{n}$(D) $\frac{2\sigma^4}{n-1}$

115年 - 第四章 直流網路分析：補充題 92-146#146599

115年 - 第三章 串並聯電路：補充題 91-144#146589

115年 - 第四章 直流網路分析：補充題 37-91#146575

115年 - 第三章 串並聯電路：補充題 41-90#146570

115年 - 第五章 電容及靜電：補充題 39-78#146547

115年 - 第六章 電感及電磁：補充題 41-100#146543

115年 - 第二章 電阻：補充題 41-119#146531

115年 - 第一章 電學基本概念：補充題 45-80#146529

114年 - 第6章 電感及電磁：6-3 電磁感應#129459

114年 - 第6章 電感及電磁：6-2 電磁效應#129455