Question

for a given data M + x bar =32,and M-xbar =2, find z​

Answer 1

Answer:

$\huge\underline\mathfrak\color{blue}..solution..$

The random variables X1, X2, ..., Xn are called a random sample of size n

from the population f(x) if X1, X2, ..., Xn are mutually independent random variables and the mar-

ginal probability density function of each Xi is the same function of f(x). Alternatively,

X1, X2, ..., Xn are called independent and identically distributed random variables with pdf f(x).

We abbreviate independent and identically distributed as iid.

Most experiments involve n >1 repeated observations on a particular variable, the first observa-

tion is X1, the second is X2, and so on. Each Xi is an observation on the same variable and each Xi

has a marginal distribution given by f(x). Given that the observations are collected in such a way

that the value of one observation has no effect or relationship with any of the other observations,

the X1, X2, ..., Xn are mutually independent. Therefore we can write the joint probability density

for the sample X1, X2, ..., Xn as

f(x1, x2, ..., xn) = f(x1)f(x2) ··· f(xn) = Yn

i=1

f(xi) (1)

If the underlying probability model is parameterized by θ, then we can also write

f(x1, x2, ..., xn|θ) = Yn

i=1

f(xi|θ) (2)

Note that the same θ is used in each term of the product, or in each marginal density. A different

value of θ would lead to a different properties for the random sample.

1.2. Statistics. Let X1, X2, ..., Xn be a random sample of size n from a population and let

T (x1, x2, ..., xn) be a real valued or vector valued function whose domain includes the sample space

of (X1, X2, ..., Xn). Then the random variable or random vector Y = (X1, X2, ..., Xn) is called a

statistic. A statistic is a map from the sample space of (X1, X2, ..., Xn) call it X, to some space of

values, usually R1 or Rn. T is what we compute when we observe the random variable X take on

some specific values in a sample. The probability distribution of a statistic Y = T(X) is called the

sampling distribution of Y. Notice that T(·) is a function of sample values only, it does not depend

on any underlying parameters, θ.

$\huge\underline\mathfrak\color{green}its..just..a example.$

$<marquee>hope this will help u..mark it as branlist </marquee>$