2. (10%)Prove the mean and variance of the normal distribution N(μ, σ²) are μ and σ², respectively.

1. (20%) Consider the following frequency table of observations on the random variable X. Based on these 50 observations, is a binomial (二項) distribution with a number of trials (n)=6 and a probability of success (p)=0.25 an appropriate model? Perform a goodness-of-fit test (適合度檢定) with α=0.05.