moharsingh
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- Oct 26, 2013
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Two cards are drawn at random with replacement from a box which contains 4 cards numbered 1,1,2 and 2.If X denotes the sum of numbers shown on the two cards,find the expected value of X.
What values do you expect after the two draws? In what proportions? Where are you stuck?Two cards are drawn at random with replacement from a box which contains 4 cards numbered 1,1,2 and 2.If X denotes the sum of numbers shown on the two cards,find the expected value of X.
This is just a matter of doing straightforward calculation. The probability you will draw a "1" on either draw is 1/2 and the probability you will draw a "2" is also 1/2. The only possible sums of two such numbers are "2", "3", and "4". To get a sum of "2" you must draw a 1 each time. What is the probability of that? To get a sum of "3" you must draw "1 then 2" or "2 then 1". What is the probability of each of those? To get a sum of "4" you must draw a "2" each time. What is the probability of that?Two cards are drawn at random with replacement from a box which contains 4 cards numbered 1,1,2 and 2.If X denotes the sum of numbers shown on the two cards,find the expected value of X.