这个作业是完成概率论相关的数学问题
MATH 525 Fall 2020
Problems:
1.一家工厂生产了N个covid测试，每个测试都有故障，概率为q。 每
测试经过质量控制，从而有可能检测出故障（如果存在）
河 令X为错误测试的数量，而Y为检测为错误的测试的数量。
显示
E（X | Y）= [nq（1- r）+（1- q）Y] /（1- qr）。
假定所有covid测试都是独立进行的。
2.考虑一个正面概率等于p的硬币。 计算预期数量
产生n个头部所需的投掷次数。
3.田野周围有17个栅栏。 其中有5个烂。
使用条件概率证明，无论腐烂桩在哪里，
连续7个职位，其中至少3个是烂的。
4. A gas station serves cars and trucks. On average, each hour 4 cars and 3 trucks arrive.
I start my observation at noon. What is the probability that the first vehicle that
arrives is a car and the first truck arrives within 15 minutes of the first car. You may
assume that the arrivals of cars and trucks are described by two independent Poisson
processes.
5. Consider a coin with probability of heads given by p. Let X be the number of tosses
until two heads in a row appear. Compute the generating function of X and use it to
compute the expectation of X in close form (i.e. without P).