Suppose that there are N different types of stickers. Once you collect all the stickers, you...

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Suppose that there are N different types of stickers. Once you collect all the stickers, you can claim a reward of 1 million dollar. Each time you get a cheetos, a compliem- ntary sticker is given. It is a gimmick to sell more cheetos. The probablity to get a sticker is equally likely as other. Let X be the number of cheetos you will need to buy before having collected all the sticker and hence claim a reward of 1 million dollar. (a) Write X as a summation of different geometric random variable. (b) Calculate E[X]. Suppose that there are N different types of stickers. Once you collect all the stickers, you can claim a reward of 1 million dollar. Each time you get a cheetos, a compliem- ntary sticker is given. It is a gimmick to sell more cheetos. The probablity to get a sticker is equally likely as other. Let X be the number of cheetos you will need to buy before having collected all the sticker and hence claim a reward of 1 million dollar. (a) Write X as a summation of different geometric random variable. (b) Calculate E[X].