The table shows the total cost c of buying t movie tickets. Write an equation to represent the relationship between c and t.

UkusakazaL
2020-10-20
Answered

The table shows the total cost c of buying t movie tickets. Write an equation to represent the relationship between c and t.

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averes8

Answered 2020-10-21
Author has **92** answers

From the table, the cost is 7 times the number of tickets so the equation is:

$c=7t$

asked 2020-11-08

Students score on a biology test is an example of which scale of measurement?

asked 2021-01-22

Quantitative/Categorical Data Identify each of the following as quantitative data or categorical data.

a. The platelet counts in Data Set 1 “Body Data” in Appendix B

b. The cigarette brands in Data Set 13 “Cigarette Contents” in Appendix B

c. The colors of the M&M candies in Data Set 27 “M&M Weights” in Appendix B

d. The weights of the M&M candies in Data Set 27 “M&M Weights” in Appendix B

a. The platelet counts in Data Set 1 “Body Data” in Appendix B

b. The cigarette brands in Data Set 13 “Cigarette Contents” in Appendix B

c. The colors of the M&M candies in Data Set 27 “M&M Weights” in Appendix B

d. The weights of the M&M candies in Data Set 27 “M&M Weights” in Appendix B

asked 2022-04-22

Given you have an independent random sample $X}_{1},{X}_{2},\dots ,{X}_{n$ of a Bernoulli random variable with parameter p, estimate the variance of the maximum likelihood estimator of p using the Cramer-Rao lower bound for the variance

So, with large enough sample size, I know the population mean of the estimator $\hat{P}$ will be p, and the variance will be:

$Var\left[\hat{P}\right]=\frac{1}{nE\left[\right((\partial /\partial p)\mathrm{ln}\hspace{0.17em}{f}_{x}\left(X\right){)}^{2}]}$

Now I'm having some trouble calculating the variance of $\hat{P}$, this is what I have so far:

since the probability function of $\stackrel{\u2015}{X}$ is binomial, we have:

${f}_{x}\left(\overline{X}\right)=\left(\genfrac{}{}{0ex}{}{n}{\sum _{i=1}^{n}{X}_{i}}\right)*{p}^{\sum _{i=1}^{n}{X}_{i}}*(1-p{)}^{n-\sum _{i=1}^{n}{X}_{i}}$

so: $\mathrm{ln}\hspace{0.17em}{f}_{X}\left(X\right)=\mathrm{ln}\left(\left(\genfrac{}{}{0ex}{}{n}{\sum _{i=1}^{n}{X}_{i}}\right)\right)+\sum _{i=1}^{n}{X}_{i}ln\left(p\right)+\hspace{0.17em}(n-\sum _{i=1}^{n}{X}_{i})\mathrm{ln}(1-p)$

and: $\frac{\partial \mathrm{ln}\hspace{0.17em}{f}_{X}\left(X\right)}{\partial p}=\frac{{\sum}_{i=1}^{n}{X}_{i}}{p}-\frac{(n-{\sum}_{i=1}^{n}{X}_{i})}{(1-p)}=\frac{n\overline{X}}{p}-\frac{(n-n\overline{X})}{(1-p)}$

and: $(\frac{\partial ln\hspace{0.17em}{f}_{X}\left(X\right)}{\partial p}{)}^{2}=(\frac{n\overline{X}}{p}-\frac{(n-n\overline{X})}{(1-p)}{)}^{2}=\frac{{n}^{2}{p}^{2}-2{n}^{2}p\overline{X}+{n}^{2}{\overline{X}}^{2}}{{p}^{2}(1-p{)}^{2}}$

since $E\left[{\stackrel{\u2015}{X}}^{2}\right]={\mu}^{2}+\frac{{\sigma}^{2}}{n}$, and for a Bernoulli random variable $E\left[X\right]=\mu =p=E\left[\stackrel{\u2015}{X}\right]$ and $Var\left[X\right]={\sigma}^{2}=p(1-p)$:

$E\left[{\left(\frac{\partial \mathrm{ln}:\left\{{f}_{X}\left(X\right)\right\}}{\partial p}\right)}^{2}\right]=\frac{{n}^{2}{p}^{2}-2{n}^{2}pE\left[\stackrel{\u2015}{X}\right]+{n}^{2}E\left[{\stackrel{\u2015}{X}}^{2}\right]}{{p}^{2}{(1-p)}^{2}}=\frac{{n}^{2}{p}^{2}-2{n}^{2}{p}^{2}+{n}^{2}({p}^{2}+\frac{p(1-p)}{n})}{{p}^{2}{(1-p)}^{2}}=\frac{np(1-p)}{{p}^{2}{(1-p)}^{2}}=\frac{n}{p(1-p)}$

Therefore, $Var\left[\hat{P}\right]=\frac{1}{nE\left[\right((\partial /\partial p)\mathrm{ln}\hspace{0.17em}{f}_{x}\left(X\right){)}^{2}]}=\frac{1}{n\frac{n}{p(1-p)}}=\frac{p(1-p)}{{n}^{2}}$

However, I believe the true value I should have come up with is $\frac{p(1-p)}{n}$.

asked 2020-11-07

Here are summary stastistics for randomly selected weights of newborn girls:

Are the results between the two confidence intervals very different?

asked 2021-01-31

Give full and correct answer for this questions Pooled variance is appropriately applied in which of the following scenarios?
A)When comparing the mean of a treatment on a single group
B)When comparing the mean of a treatment on two groups
C)When comparing the means of three or more treatments on two groups
D)When comparing the means of two treatments on three or more groups

asked 2022-01-19

What is the difference between probability distribution and sampling distribution?

asked 2022-06-02

The thickness of a non-spreadable liquid between two surfaces

There's this question I've come to when doing my research when working on polymer brushes; what I'm looking for is to find my reaction mixture thickness between two plates. So the setup is as follows: My bottom plate, with initiator on it. Then I put a drop of my reaction mixture on it which does not spread. Lastly, I put the top plate and the drop fills the gap between two plates and forms a film. I know how much the top plate weighs and the surface tension of drop and two plates, how can I calculate the film thickness between two plates? Here's my thought processes:

1.Should I look at the problem unsteady or steady? When thought of steady, I tried to equalize hydrodynamic pressure and weight of top plate but that did not match for the data of a paper working close to my work. They don't mention how they calculated their thickness.

2.Can I think of it simplistically? Like I know the volume of the drop that I put, I know the surface of the plate, then divide the volume by surface to get film thickness?

There's this question I've come to when doing my research when working on polymer brushes; what I'm looking for is to find my reaction mixture thickness between two plates. So the setup is as follows: My bottom plate, with initiator on it. Then I put a drop of my reaction mixture on it which does not spread. Lastly, I put the top plate and the drop fills the gap between two plates and forms a film. I know how much the top plate weighs and the surface tension of drop and two plates, how can I calculate the film thickness between two plates? Here's my thought processes:

1.Should I look at the problem unsteady or steady? When thought of steady, I tried to equalize hydrodynamic pressure and weight of top plate but that did not match for the data of a paper working close to my work. They don't mention how they calculated their thickness.

2.Can I think of it simplistically? Like I know the volume of the drop that I put, I know the surface of the plate, then divide the volume by surface to get film thickness?