Page - 49 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

2.7 Exercises 49 c) Generate all the combinations of throwing two dice (the number of eyes can vary from1 to 6). Count howmany combinationswhere the sumof the eyes equals7. Filename:combine_sets.py. Exercise2.13: Frequencyofrandomnumbers Writeaprogramthat takes apositive integerN as input and thendrawsN random integers in the interval Œ1;6 (bothends inclusive). In theprogram,counthowmany of thenumbers,M, that equal6andwriteout the fractionM=N .Also,print all the randomnumbers to the screen so that youcan check foryourself that the counting is correct. Run theprogramwith a small value forN (e.g.,N = 10) to confirm that itworksas intended. Hint Userandom.randint(1,6) todrawarandomintegerbetween1and6. Filename:count_random_numbers.py. Remarks For largeN , this programcomputes theprobabilityM=N of getting six eyeswhen throwingadie. Exercise2.14:Game21 Consider some game where each participant draws a series of random integers evenlydistributed from0and10,with the aimof getting the sumas close as pos- sible to 21, but not larger than 21. You are out of the game if the sumpasses 21. Aftereachdraw,youare told thenumberandyour total sum,andareaskedwhether youwantanotherdrawornot. Theonecomingclosest to21 is thewinner. Implement thisgameinaprogram. Hint Userandom.randint(0,10) todrawrandomintegers in Œ0;10 . Filename:game_21.py. Exercise2.15:Linear interpolation Somemeasurementsyi, i D 0;1;:: :;N (givenbelow), of a quantityy havebeen collected regularly, once everyminute, at times ti D i, i D 0;1;:: :;N . Wewant tofind thevaluey in between themeasurements, e.g., at t D 3:2min. Computing suchy values is called interpolation. Letyourprogramuse linearinterpolation tocomputeybetweentwoconsecutive measurements: 1. Find i such that ti t tiC1. 2. Findamathematical expressionfor thestraight line thatgoes through thepoints .i;yi/and .iC1;yiC1/. 3. Compute they valueby inserting theuser’s timevalue in theexpression for the straight line. a) Implement the linear interpolation technique in a function that takes an array with theyi measurements as input, togetherwith some time t, and returns the interpolatedy valueat time t.