Please help

Suppose the following is the probability distribution function of random variable Y: gify=1 y): iify=2 gifyzs For all the subparts of this question, you should assume that sampling from this distri bution is random. For this question and only this question you do not need to show your work. You may nd it helpful to use excel for some parts of this question. Define the sample mean as: _ 1 \" yEyi And, dene the sample variance as: 1 2_ _ ,2 371 1:(yz_y) i=1 (a) (2 points) If you draw a random sample of size n : 3, what is the probability of drawing a sample where g : 2 (b) (2 points) If you draw a random sample of size n : 3, what is the probability of 5 drawing a sample where g : 5 (c) (2 points) If you draw a random sample of size n : 3, what is the probability of drawing a sample where 52 : 0 (d) (2 points) If the sample size is n : 4, what is E [g]? (e) (2 points) If you draw a random sample of size n : 4, what is var (g)? (f) (2 points) If you draw a random sample of size n : 4, what is E [32]