Resolved: "We have a data set (n=100) with hormone..."

Cheyanne Leigh

Answered question

2020-11-26

We have a data set (n=100) with hormone concentrations and the frequency of each value. Assuming normal (continuous) distributions, We need to determine the parameters of the continuous probability distribution functions.

Answer & Explanation

ottcomn

Skilled2020-11-27Added 97 answers

Step1
Let us suppose

X_{1}, X_{2}, \dots ., X_{100}

are samples from normal distribution
with mean

μ and v a r i a n c e σ^{2}

Hence,

X_{i} \sim N (μ, σ^{2})

Here note that

μ and σ^{2}

are the parameters of the probability distribution
Now, You have calculated mean, Variance, and standard deviation of the samples.
Sample mean,

\overset{―}{X} = \frac{1}{100} \sum_{i} X_{i}

,
sample variance ,

S^{2} = \frac{1}{100 - 1} \sum_{i = 1}^{100} {(X_{i} - \overset{―}{x})}^{2} N o w, E (\overset{―}{x}) = \frac{1}{100}

\sum_{i} (X_{i}) = \frac{1}{100} \times 100 \times μ = μ

and it can be shown

E (S^{2}) = σ^{2}

Step 2
Hence, the sample mean and sample variance are the estimates of the population parameter

μ and σ^{2}

The parameters of the probability distribution will be sample mean that you have calculated and sample variance that you have calculated.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Didn't find what you were looking for?