Probstat/week4 practice 2
- This is part of probstat.
Useful properties
1. For a random variable X and constants a and c, prove that E[aX+c]=aE[X] + c.
2. Let X be a random variable and , prove that .
![{\displaystyle \mu ={\mathrm {E} }[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d988be241dd4f2aba51e76f922ca04363c2956a)
![{\displaystyle {\mathrm {E} }[X-\mu ]=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c91fbd56166a5c0ce17edf3e7be8e0cebc377e8c)
Dinner dish experiment
Recall the dinner experiment: n people are having a dinner at the table with a rotating turntable. Each person orders one different dish and gets her/his order exactly in front of her/him. They decide to randomly rotate the turntable so that each one of them will get a random dish. Let random variable Y be the number of people who get their own dish after the random rotation.
1. Find .
![{\displaystyle {\mathrm {E} }[Y^{2}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd58017689939e40cc9487e83035216581ab62a4)
