Organize a charity event

专题: Probability / 概率
难度: L4
来源: QuantQuestion

题目详情

为了举办一场成本为 $100\mathrm{K}$ 的慈善活动，某组织开始募款。捐款人依次独立捐款，每位捐款金额服从均值为 $20\mathrm{K}$ 的指数分布。一旦累计捐款达到或超过 $100\mathrm{K}$ ，募款过程停止。求达到至少 $100\mathrm{K}$ 所需捐款人数的分布、均值和方差。

To organize a charity event that costs $100\mathrm{K}, an organization raises funds. Independent of each other, one donor after another donates an amount of money that is exponentially distributed with mean$ 20\mathrm{K}. The process is stopped as soon as $100\mathrm{K} or more has been collected. Find the distribution, mean, and variance of the number of donors needed until at least$ 100\mathrm{K} has been collected.

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