I am trying to learn more about statistics and wanted to ask the following questions:-

1) Are the following terms mean the same thing:-

Normal Distribution= Gaussian Distribution

2) Does a Normal Distribution data set only contain random error and is free from systematic errors (assume perfect world).

3) I am trying to plot a bell shaped curve for a Normal Distribution data set of 30 measurements with a mean of 40.1484 and a SD of 1.5.

I sort my data into low to high and add the average in the middle but the plot does not show a bell shaped curve (see attached).

How can I plot my measurements to show a bell shaped curve (I have been assured that the data set is a

Thank you.

I'm not trained in mathematics, but I need to explain the following in such terms. Could you please assist?

- Three values are ranked ordinally (1 to 3) in terms of importance.
- Therefore: Value 1 > Value 2 > Value 3
- Each value carries the same weight. The sum of weights = 1. Therefore the individual weight is 1/3=0.33
- The ordinal importance is inversely proportional to the value's rank and is calculated as such: 1/(value weight*value rank) e.g. for value 1 which is the most important, the ordinal importance is: 1/(0.33*1)=3
- The sum of the ordinal importance values allows the relative importance (or the influence probability) to be calculated, which is essentially a percentage value. E.g. Value 1 influence probability is calculated: 3/(3+1.5+1)*100=54.5%

The table below summarises each value's parameters:

Value | Ordinal importance | Influence Probability |

1 | 3 | 54.5 |

2 | 1.5 | 27.3 |

3 | 1 | 18.2 |

If we plot the values graphically we have the following:

Values 3.jpg

What is already obvious is that we have a curve that is progressively flattening. Now if we extend the number of values to say 12, the progressive flattening of the curve is clearer.

Values 12.jpg

So here is my question: What is the nature of this function? I think it may be something like an inverse natural log (or whatever - I don't know).

I need to explain this in words so that if we didn't have the benefit of the images, that a mathematician would immediately understand what I am referring to.

Thank you maths gurus!

Gareth

94 hurricanes

* Assume that the sample data satisfies all assumptions for linear regression.

> summary(model)

Call:

lm(formula = Damage ~ Landfall.Windspeed)

Residuals:

Min 1Q Median 3Q Max

-9294 -4782 -1996 -531 90478

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -10041.78 6064.29 -1.656 0.1012

Landfall.Windspeed 142.07 56.65 2.508 0.0139 *

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12280 on 92 degrees of freedom

Multiple R-squared: [ A ], Adjusted R-squared: 0.05381

F-statistic: 6.289 on 1 and 92 DF, p-value: 0.01391

(1) Write the equation for the linear model using the variables Damages and

Landfall.Windspeed, taking the results of the t-tests into account.

(2) Pearson’s correlation coefficient for Damages and Landfall.Windspeed

is 0.2529438. Calculate and interpret the value of R 2 in relation to the predictor and

response variables.

................................

Part 1

The question is worded in such a way as to use RStudio but in Rstudio

summary(model)

Error in summary(model) : object 'model' not found

I do not understand how to get the equation without any x or y data.

I am sure I am supposed to reverse it out somehow but I cannot figure out how.

y^ = 142.07 -10041.78x

but that is incorrect because I am not using real data, thats estimated.

Question 2 boils down to the same issue.

How do I reverse my x and y data from the provided data in the question so I can produce the proper equation? ]]>

the higher the speed energy value, the higher chance for the horse to win the game. And what I want to do is to map this group of numbers into odds and compare it with the provided odds given by the bookmaker.

the horse with negative speed energy value is considered unlikely to win the game.

A sample is listed below. We can see the given odds it ranged from 3.5 to 75, and I want to simulate a table based on the speed energy value into another group of odds in similar range.

Thanks for the help and sorry for my poor english.

Horse No. | Speed Energy Value | Winning Odds Provided by the bookmaker |

1 | -1 | 20 |

2 | 3 | 3.5 |

3 | 1 | 7.2 |

4 | 5 | 31 |

5 | 4 | 48 |

6 | 1 | 4.9 |

7 | -1 | 4.9 |

8 | 0 | 13 |

9 | 2 | 14 |

10 | -2 | 14 |

11 | -3 | 75 |

12 | 1 | 17 |

a. 50%

b. 37.5%

c. 62.5%

d. 12.5%

e. none of these

Confused in solving this one from GRE. ]]>

The number of car accidents that happen in a specific region

Calculate (approximately) the probability to wait more than 60 days for the occurrence of the 40th car accident.

Consider X=number of car accidents. Then X follows Poisson distribution with λ=0.5 and P(X=1)=0.3032

I consider the random variable Y=number of days till the 40th car accident

Then Y follows Negative Binomial(k=40,p=0.3032) and the asked probability is P(Y>60).

Is my solution right? ]]>

Problem 26. PMF of the minimum of several random variables.

On a given day. your gold score takes values from the range 101 to 110. with probability 0.1, independent of other days. Determined to improve your score, you decide to play on three tdifferen days and declare as your score the minimum X of the scores X1, X2 nd X3 on the different days.

(a) Calculate the PMF of X.

(b) By how much has your expected score improved as a result of playing on three days?

Solution to Problem 2.26.

(a) The possible values of the random variable X are the ten numbers 101, ..., 110, and the PMF is given by

Code:

`px(k) =`

P(X > k - 1) - P(X > k), if k = 101, ...110,

0, otherwise.

Code:

`P(X > k) = P(X1 > k, X2 > k, X3 > k)`

= P(X1 > k)P(X2 > k)P(X3 > k)

= (110 - k)^3 / 10^3

Code:

`px(k) =`

((111 - k)^3 - (110 - k)^3) / 10^3, if k = 101, ...110,

0, otherwise.

I understand the given answer numerically. But still it feels like magic to me.

I split the possible values of X1, X2, X3 into three sections (on a number line):

Code:

`First: X <= k - 1`

Second: X > k - 1 and X <= k

Third: X > k

The second section is the probability that the answer is finding.

The third section shows up in the equation with P(X > k).

So as i read it when i have the formula

P(X > k - 1) - P(X > k)

Then P(X > k - 1) is second and third section

and

P(X > k) is the third section

By subtraction P(X > k - 1) - P(X > k) is then just the second section.

I made a venn diagram (with squares) in which the rows are X1, X2, X3 (independent of course). And the columns are the sections on the number line.

1oxeMEb.jpg

If i now want to answer a DIFFERENT question. What is the chance that each X1, X2, X3 is at least K? I put the following formula:

((B or C) - C) * ((E or F) - F) * ((G or I) - I) = B * E * H

This i understand.

When i look at the ORIGINAL question, what is the chance that ONE of X1, X2, X3 is at least K? I put this formula:

((B or C)*(E or F)*(G or I)) - (C * F * I)

Geometrically the two formula's give me the same pieces on the venn diagram.

First formula: first row, second column and second row, second column and third row, second column = second column

Second formula: second column and third column - third column = second column

Like i said before, i understand the original answer numerically. But i'm trying to understand it in different ways (in my case the venn diagram), because i don't find it intuitive at all. Does someone have another way to understand this answer. With venn diagram or another solution alltogether?

thanks for the help

Hey! First of all, I'm terribly sorry if this is in the wrong category! I'm not sure where this fits in.

I'd like some help with understanding binominal coefficients.

So, if I've understood it correctly, the general formula for any binominal coefficient is

(n choose k) = n!/k!(n-k)!

But I'm having trouble understanding the logic behind the formula. I understand that putting your desired numbers k and n in said formula will give the correct answer, but why is that? How can you see from looking at the formula that it'll give you the amount of different k's in n? Additionally, as I've understood it, any binominal coefficients where the second integer is 2 will always give

(n choose 2) = n(n-1)/2

Is this just because the general formula always gives that answer, or is there another reason? Why just n(n-1)? I was originally thinking it had something to do with the fact that n! = n*(n-1)!, but that wouldn't seem to be the case, given that, in the formula, n(n-1) isn't factorial. Also, why divided by 2? Is that also just because applying the general formula will always leave 2 as the denominator, in this case, or is there another way to realize that?

Sorry if I'm unclear, and again, if I'm in the wrong category.

Thanks in advance!

]]>I'd like some help with understanding binominal coefficients.

So, if I've understood it correctly, the general formula for any binominal coefficient is

(n choose k) = n!/k!(n-k)!

But I'm having trouble understanding the logic behind the formula. I understand that putting your desired numbers k and n in said formula will give the correct answer, but why is that? How can you see from looking at the formula that it'll give you the amount of different k's in n? Additionally, as I've understood it, any binominal coefficients where the second integer is 2 will always give

(n choose 2) = n(n-1)/2

Is this just because the general formula always gives that answer, or is there another reason? Why just n(n-1)? I was originally thinking it had something to do with the fact that n! = n*(n-1)!, but that wouldn't seem to be the case, given that, in the formula, n(n-1) isn't factorial. Also, why divided by 2? Is that also just because applying the general formula will always leave 2 as the denominator, in this case, or is there another way to realize that?

Sorry if I'm unclear, and again, if I'm in the wrong category.

Thanks in advance!

as for problem #3: a researcher wants to know if there is a relationship between stress level and hair loss. Stress measures on a scale of 0 to 10. Use this data to test if there is a relationship at the a=0.05 level. Traditional method.

Stress level | 7 | 1 | 10 | 7 | 3 | 6 | 2 | 2 | 9 | 4 |

Hair loss (oz) | 0.1 | .05 | .09 | .08 | .02 | .07 | .01 | .05 | .11 | .05 |

H1:

critical value(s):

Test Value (from calculator):

decide:

conclude:

This is easy enough to demonstrate. If you have 20 agents handling 6 calls per hour over 7 working hours, you will have a daily throughput of 840 calls. If you can lift the base number by just one – from six to seven calls per hour – your daily call rate climbs to 980 calls. That’s a weekly increase of 700 calls, the equivalent of an

Thank you in advance for any help.

Best,

Chris ]]>

For a random variable X that follows a normal distribution with an unknown mean μ, variance of 2 and P(X<7)=P(X>14), what is the probability P(X<=10)?

The possible answers are:

A. 0.5987 B. 0.5 C. 0.4013 D. 0.8413

I have one equation with one unknown variable, so I can't calculate the asked probability. Any ideas? ]]>

Say that X1=X2 which means that the random variable X1 and X2 are equal in distribution. This means that these two random variables have the same distribution, same mean and same variance. These two random variables are independent. Is it true that X1+X2=2X1?

In my head this makes perfect sense but i am having trouble writing a proof to this. ]]>

Suppose people randomly pick a number between 0 and 1. What would be the expected number of people you would have to ask for numbers if you want the sum to be greater than 1 for the 1st time?

Steve ]]>

We also have a TOTAL of 100$ that we must distribute on those 5 levels(we must use all 5 levels)

How can we calculate the optimal way to distribute the 100$ to get

the highest procent?

(I have about 30 levels so I am after a function to use)

Thank you!