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Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite 1 It is a question 59 on page 87 from Ross's book (Introduction to Probability Models) Let $X_1,X_2,X_3,X_4$ are independent continuous random variables with a common distribution function F and let $p = P(X_1 < X_2 > X_3 < X_4)$ Just as the Title, what does it mean? Or similar questions with such an inequity? Thanks Update 1 : The solution says: Use the fact that F(Xi) is a uniform (0,1) random variable to obtain. But where is this fact ? Update: A similar question How can I compute an expression for $P(X_1>X_2>X_3>X_4)$ if $X_1,X_2,X_3,X_4$ are normal and mututally independent? BTW I am not a native-English speaker, and I am learning it by myself. probability share | cite | improve this question edited Aug 24 at 9:01 asked Dec 27 '17 at 13:37 evergreenhomeland 82 8 Usually, a "multiple" inequality is a conjucntion: $X_1 < X...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite A pumpkin is thrown-up from a MIT building as shown in 1st graph. 2nd graph is of its velocity (first derivative) and 3rd one is of acceleration (2nd derivative). PROBLEM: I can't relate the reality of the motion of the pumpkin with the graphs. Reality of Velocity: When we throw the pumpkin, its speed (velocity) starts to decrease and become zero at top and then speed starts to increase but since velocity is speed with direction and direction is downwards, hence velocity graph is going down. This means increase in velocity is being represented as negative number and a downward graph, I wonder how will one represent decreasing velocity, with a positive number and upward direction ?) Reality of Acceleration: Going up pumpkin is de-accelerating (decreasing) and going down it is accelerating (increasing) but graph is constant, just straight line. By looking only at the graph of acceleration and without looking ...