機率分佈與統計推論的基礎理論與應用

📝 歷屆考古題

• 112年 hce_nthu 第16題
  Kim is at a train station, waiting to make a phone call. Two public telephone booths, next to each o…
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• 112年 hce_nthu 第17題
  Let $X$ and $Y$ be independent random points from the interval (-1, 1). Find $E(\max(X, Y))$.
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• 112年 hce_nthu 第18題
  A stick of length 1 is broken into two pieces at a random point. Find the correlation coefficient an…
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• 112年 hce_nthu 第19題
  A traffic light can be in one of the three states: Green (G), Red (R), and Yellow (Y). The light cha…
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• 112年 hce_nthu 第20題
  Let $X_1, X_2, \dots, X_n$ be $n$ identical and independently distributed exponential random variabl…
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• 112年 hce_nthu 第21題
  $Y_1, Y_2, \dots$ are independent and identically distributed random variables; the moment generatin…
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• 112年 hce_nthu 第22題
  A newly married couple decides to continue having children until they have one of each sex. If the p…
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• 112年 hce_nthu 第23題
  The two random variables, $X$ and $Y$, are independent and exponentially distributed, each with mean…
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• 112年 hce_nthu 第24題
  We have some earthquake data that occurred in a region over years, summarized in the following table…
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• 112年 hce_nthu 第25題
  Which of the following statements are correct? (1) Statistical independence implies no correlation (…
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• 112年 hce_nthu 第26題
  Hospital A is experimenting with an AI-assisted system for judging the status (+ or -) of a certain…
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• 112年 hce_nthu 第27題
  Based on the playing history of Team A and Team B, Team A has a 60\% chance of winning basketball in…
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• 112年 hce_nthu 第28題
  From the general knowledge, the population occurrence rate of asthma is 0.1 for children who visit h…
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• 112年 hce_nthu 第29題
  A histogram of a dataset X is plotted in Figure (i). The $1^{st}$ quartile, median and the $3^{rd}$…
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• 112年 hce_nthu 第30題
  Which of the following is NOT a reason for conducting the paired-sample T-test?
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• 111年 hce_nthu 第16題
  Suppose that $X$ and $Y$ are exponential random variables that are independent of each other. Both $X$…
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• 111年 hce_nthu 第17題
  Suppose that the joint cumulative distribution function of the lifetimes of two smart watches is giv…
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• 111年 hce_nthu 第18題
  Suppose that the random variables $X_1, X_2,...$ are independent of each other. Each of these random…
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• 111年 hce_nthu 第19題
  If $Y$ is uniformly distributed over $[0, 5]$, what is the probability that the roots of the equatio…
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• 111年 hce_nthu 第20題
  The moment generating function of $X$ is given by $M_X(t)=e^{2e^t-2}$ and that of $Y$ by…
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• 111年 hce_nthu 第21題
  A smooth-surface table is ruled with equidistance parallel lines, a distance $D$ apart. A needle of…
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• 111年 hce_nthu 第22題
  Consider the set of all families with two children. Randomly select one family. Assume that in a two…
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• 111年 hce_nthu 第23題
  Recently, Larry taught his daughter Emily how to play a game. To encourage Emily to practice this ga…
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• 111年 hce_nthu 第24題
  There are 2 exams in Statistics class. The midterm score (X) is approximately normal distributed wit…
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• 111年 hce_nthu 第25題
  Suppose we are interested in the rate ($p$) of Cancer A in rats that have been fed with a diet consi…
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• 111年 hce_nthu 第26題
  In a statistics exam, all problems are multiple-choice with 5 possible items (5選項之單選題), e.g., (A)(B)…
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• 111年 hce_nthu 第27題
  Suppose $X_i$ independently follows a Poisson distribution with mean 3 for $i = 1 \sim 1000$. What i…
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• 111年 hce_nthu 第28題
  Suppose we want to investigate the relationship between the heights of students and the sport teams…
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• 111年 hce_nthu 第29題
  According to the following plots of three variables X1, X2, and Y from the data set, please select t…
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• 111年 hce_nthu 第30題
  The following is a joint probability table between two categorical variables, the education level an…
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