Question

Suppose X1,X2, ..., Xn be a sequence of idpendently identically distributed random variables with mean 4 and variance 16. Let S =X1+X2+...+Xn, Z1=sqrt(n)S/4, Z2=(S-4)/16, and Z3=sqrt(n)(S/n-4)/4. Then ...

Answer 1

Step-by-step explanation:

Theorem If X1 , X2, ..., Xn are independent and identically distributed standard uniform random variables, then X(r) has the beta(β,γ) distribution where β = r and γ = n - r + 1. X := UniformRV(0, 1); Y := OrderStat(X, r, n); PDF(Y); yield the probability density function of a beta(r, n - r + 1) random variable

Answer 2

Indicators are organic weak acids or bases with complicated structures. For simplicity, we represent a general indicator by the formula HIn

, and its ionization in a solution by the equilibrium,