If

Falak Kinney
2021-10-20
Answered

Random variables $X}_{1},{X}_{2},\dots ,{X}_{n$ are independent and identically distributed; 0 is a parameter of their distribution.

If$X}_{1},{X}_{2},\dots ,{X}_{n$ are Normally distributed with unknown mean 0 and standard deviation 1, then $\stackrel{\u2015}{X}\sim N\left(\frac{0,1}{n}\right)$ . Use this result to obtain a pivotal function of X and 0.

If

You can still ask an expert for help

Adnaan Franks

Answered 2021-10-21
Author has **92** answers

Since $X}_{1},{X}_{2},\dots ,{X}_{n$ are IID random Variables such that,

$\stackrel{\u2015}{X}\sim N(0,\frac{1}{n})$

This implies

${X}_{i}\sim N(0,1)$

Now,

Pivotal function for Mean can be written as

$Z=\frac{(\stackrel{\u2015}{x}-\mu )}{\frac{\sigma}{\sqrt{n}}}=\frac{(\stackrel{\u2015}{x}-0)}{\frac{1}{\sqrt{n}}}$

This implies

Now,

Pivotal function for Mean can be written as

asked 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a

Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places

asked 2021-03-18

A population of values has a normal distribution with

Find the probability that a single randomly selected value is between 133.6 and 134.1.

Write your answers as numbers accurate to 4 decimal places.

asked 2022-01-19

How can you find standard deviation from a probability distribution?

asked 2021-06-03

Assume that X and Y are jointly continuous random variables with joint probability density function given by

$f(x,y)=\{\begin{array}{l}\frac{1}{36}(3x-xy+4y)\text{}if\text{}0x2\text{}and\text{}1y3\\ 0\text{}\text{}\text{}\text{}\text{}othrewise\end{array}$

Find the marginal density functions for X and Y .

Find the marginal density functions for X and Y .

asked 2022-01-27

He following table shows the probability distribution for a discrete random variable. What is the variance of X?

X 11 14 16 19 21 23 24 29

P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08

The mean of the discrete random variable X is 18.59.

X 11 14 16 19 21 23 24 29

P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08

The mean of the discrete random variable X is 18.59.

asked 2021-03-01

A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size $n=153$ is drawn.

Find the probability that a sample of size$n=153$ is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places.

P=?

Find the probability that a sample of size

P=?

asked 2022-01-28

What are the mean and standard deviation of a probability density function given by $Pr(X=k)=\frac{{3}^{k}{e}^{-3}}{k!}$ for $k\in \{0,1,2...\mathrm{\infty}\}$ ?