第 2 / 3 页
非代码面试题
显示 20 / 48 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
2962Sup-Norm Distance Below One QuarterTwo independent random points are drawn uniformly from the unit square. What is the probability that their L distance is at most 1/4?概率中等derivation未尝试面试订阅2963Closer to the Center Than to the Left EdgeA random point (X,Y) is uniform in the unit square. What is the probability that the point is closer to the center (1/2,1/2) than to the left edge x=0?概率困难derivation未尝试面试订阅2964Expected Area of the Rectangle to the OriginA random point (X,Y) is uniform in the unit square. Consider the axis-aligned rectangle with opposite corners at (0,0) and (X,Y). What is the expected area of that rectangle?概率简单derivation未尝试面试订阅2965Exactly One Point in the Middle ThirdTwo independent random points are drawn uniformly from [0,1]. What is the probability that exactly one of them falls in the middle third interval [1/3,2/3]?概率简单derivation未尝试面试订阅2966Longer Piece Above Two ThirdsA unit stick is cut once at a uniformly random point. What is the probability that the longer piece has length more than 2/3?概率简单derivation未尝试面试订阅2967Both Pieces Longer Than One FifthA unit stick is cut once at a uniformly random point. What is the probability that both resulting pieces have length greater than 1/5?概率简单derivation未尝试面试订阅2968Expected Shorter Piece from One CutA unit stick is cut once at a uniformly random point. Let S be the length of the shorter piece. Compute E[S].概率简单derivation未尝试面试订阅2969Expected Product of the Two PiecesA unit stick is cut once at a uniformly random point. If the two piece lengths are U and 1-U, compute E[U(1-U)].概率简单derivation未尝试面试订阅2970Expected Absolute Imbalance After One CutA unit stick is cut once at a uniformly random point. Let D be the absolute difference between the two resulting lengths. Compute E[D].概率简单derivation未尝试面试订阅2971Three Pieces All Longer Than One FifthTwo cut points are drawn independently and uniformly on [0,1], and the stick is cut at the ordered locations. What is the probability that all three resulting pieces have length greater than 1 5 ?概率中等derivation未尝试面试订阅2973Triangle Condition for a Broken StickTwo cut points are drawn independently and uniformly on [0,1], and the stick is cut into three pieces. What is the probability that the three pieces can form a triangle?概率中等derivation未尝试面试订阅2974Longest Piece Shorter Than Two ThirdsTwo cut points are drawn independently and uniformly on [0,1]. After ordering them, the stick is split into three pieces. What is the probability that the longest piece has length less than 2/3?概率中等derivation未尝试面试订阅2975Expected Shortest Piece with Two CutsTwo cut points are drawn independently and uniformly on [0,1], then ordered to form three stick pieces with lengths X 1,X 2,X 3. Compute E[\min(X 1,X 2,X 3)].概率中等derivation未尝试面试订阅2976Expected Longest Piece with Two CutsTwo cut points are drawn independently and uniformly on [0,1], then ordered to form three stick pieces with lengths X 1,X 2,X 3. Compute E[\max(X 1,X 2,X 3)].概率中等derivation未尝试面试订阅2977Expected Sum of Squared Piece LengthsTwo cut points are drawn independently and uniformly on [0,1], then ordered to form three stick pieces with lengths X 1,X 2,X 3. Compute E[X 1 2+X 2 2+X 3 2].概率中等derivation未尝试面试订阅2978Expected Product of the Three PiecesTwo cut points are drawn independently and uniformly on [0,1], then ordered to form three stick pieces with lengths X 1,X 2,X 3. Compute E[X 1X 2X 3].概率中等derivation未尝试面试订阅2979Leftmost Piece Exceeds One HalfTwo cut points are drawn independently and uniformly on [0,1] and ordered. Let L be the leftmost piece length. What is P(L>1/2)?概率中等derivation未尝试面试订阅2980Expected Leftmost Piece LengthTwo cut points are drawn independently and uniformly on [0,1] and ordered. Let L be the leftmost piece length. Compute E[L].概率中等derivation未尝试面试订阅2981Size-Biased Piece from Two CutsTwo cut points are drawn independently and uniformly on [0,1], forming three pieces with lengths X 1,X 2,X 3. A random point is then drawn uniformly on the stick, and you keep the piece containing that point. Let B be its length. Compute E[B].概率困难derivation未尝试面试订阅2982Second Moment of a Size-Biased PieceIn the same setup as above, a random point is drawn on the stick after two cuts and B is the length of the piece containing that point. Compute E[B 2].概率困难derivation未尝试面试订阅