Riemann surface
matlab

1.4 EXERCISES
1.1. Describe a potential data analysis in engineering where parametric methods are appropriate. How would you defend this assumption?
1.2. Describe another potential data analysis in engineering where parametric methods may not be appropriate. What might prevent you from using parametric assumptions in this case?
1.3. Describe three ways in which overconfidence bias can affect the statistical analysis of experimental data. How can this problem be overcome?

2.10 EXERCISES
2.1. For the characteristic function of a random variable $X$, prove the three following properties:
(i) $\varphi_{a X+b}(t)=e^{i b} \varphi x(a t)$.
(ii) If $X=c$, then $\varphi x(t)=e^{i c t}$.
32 PROBABILITY BASICS
(iii) If $X_1, X_2, X_n$ are independent, then $S_n=X_1+X_2+\cdot+X_n$ has characteristic function $\varphi_m(t)=\prod_{i=1}^n \varphi X_i(t)$.
2.2. Let $U_1, U_2, \ldots$ be independent uniform $\mathcal{U}(0,1)$ random variables. Let $M_n=\min \left{U_1, \ldots, U_n\right}$. Prove $n M_n \Longrightarrow X \sim \mathcal{E}(1)$, the exponential distribution with rate parameter $\lambda=1$.
2.3. Let $X_1, X_2, \ldots$ be independent geometric random variables with parameters $p_1, p_2, \ldots$. Prove, if $p_n \rightarrow 0$, then $p_n X_n \Longrightarrow \mathcal{E}(1)$.

E-mail: help-assignment@gmail.com  微信:shuxuejun

help-assignment™是一个服务全球中国留学生的专业代写公司