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A box contains seven chips, each of which is numbered (one number on each chip). The number 1 appears on one chip. The number 4 appears on one chip. The number 2 appears on three chips. The number 3 appears on two chips. Two chips are to be randomly sampled from the box without replacement. Let X be the sum of the numbers on the two chips to be sampled. (a) Write out all of the possible outcomes for this experiment, together with the corresponding X values. Give the probability function for X. (Note that the number of outcomes will be different in part (a), depending upon whether you use combinations or permutations, but the probability function for X in part (b) will be the same). Calculate E(X)-px , V(X)-0x2 , and ơx. When two chips are randomly sampled from the box without replacement, what can you expect the sum of the numbers on the two chips selected to be? If this experiment is to be performed 8600 times, (i) (b) (c) (d) (e) how many times out of the 8600 trials will the numbers on the two chips selected sum to 4? what will the numbers on the 17200 chips selected sum to? (ii)

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he posible out cemes, ase Griven, x 3,4,5,6, : . The probability distribution of x is, 3 2. 1 ,2구 at ス! ス! 只1 沒( Vaa(x): E(x)-E2(x): 24952h-(48571) .36lo ④ Expected sum of numbesg: h8571 @naoox읊 : ho95.238-4095 a l

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