# Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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### Yule Walker equations

The Yule-Walker equations relate the auto covariance of a random signal to the autoregressive (AR) model parameters. They can be used to estimate AR models from data by first estimating the auto ...
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### Hypothesis testing question

The article “Statistical evidence of discrimination” (J. Ameri. Stat. Assoc., 1982, 773-83) discussed the court case of Swain v Alabama (1965), in which it was alleged that there was discrimination ...
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### Largest Number Drawn - Why are These Approaches Not Equivalent?

Here's the question: Four numbers are drawn at random from a box of ten numbers 0, 1, ..., 9. Find the probability that the largest number drawn is a six if the draws are made with replacement. The ...
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### Calculating lambda in statistics

I am trying to figure out how to find lambda for a question: Compute the probability of taking at least 7 minutes to receive a call. The exponential mean is 5.
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### Prove $\sum_i \frac{\bar{x}(x_i-\bar{x})}{nS_{xx}} =0$

Prove $$\sum_i \frac{\bar{x}(x_i-\bar{x})}{nS_{xx}} =0$$ That is one detail in a proof of the variance of the intercept $\alpha$ in the simple linear regression $Y_i=\alpha+\beta x_i$.
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### How would I solve this poker statistics question with an infinite deck?

My professor threw out this question for the class as an extra credit question. I'm not asking for an answer, but rather, a nudge in the right direction to solve the problem. I'm currently stuck ...
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### Prove $SST=SSE+SSR$

Prove $$SST=SSE+SSR$$ I start with $$SST= \Sigma (y_i-\bar{y})^2=...=SSE+SSR+ \Sigma 2( y_i-y_i^*)(y_i^*-\bar{y} )$$ and I don't know how to prove that $\Sigma 2( y_i-y_i^*)(y_i^*-\bar{y} )=0$ a ...
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### regression on circular data

How would one design a regression where the dependent variable is measured in degrees on a circle? The dependent variable is on the range [0, 360), and the independent variables are demographic ...
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### how to calculate p value of 2 sample

James and Margaret grow watermelons. Margaret claims her watermelons are heavier than James's watermelons. $40$ sample has been taken from both. James: mean $7.3$ variance $0.4$ Margaret mean $11.3$ ...
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### How many strings in the letters a, b, and c have length 10 and exactly four a's?

part a) How many strings in the letters a, b, and c have length 10 and exactly four a's? I did $\binom{10}{4} = 210$ different ways for the strings of length $10$ in part a to be arranged, but I'...
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### Same mean, different standard deviation in data sets

How would a data set containing the values of a variable with a mean of 50 and a standard deviation of 3 compare with another data set containing the same variable, but a mean of 50 and a standard ...
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### Find the probability that a person has a headache given that the person has a fever.

For the problem below are we going to use the equiprobable space. Which is in particular, if $S$ contains n points then the probability of each point is $1/n$. For an event $A$, $P(A) =$ (number of ...
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### Uncertainty in parallel resistors.

I need help with one of my study guide questions. We learned about uncertainty in class but am not sure how to attack this problem: Could someone walk me through this example? Any help will be ...
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### Calculate variance

I was given this question as HW: A survey reveals that on average 1 computer out of 800 computers crashes during a severe thunderstorm. A certain company had 4,000 working computers when the ...
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### Probability density function of random variables.

I need help with one of my study guide questions. We learned a bit about PDF but I am not sure how to combine them. Here is the problem: Could anyone walk me through how to do this? Any help will be ...
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### Probability and proportion from standard deviation and mean [duplicate]

I do not know how to start this problem-help needed-kindly help me The lifetimes of a colour TV picture tube is normally distributed, with a mean of 8 yrs and a standard deviation of 2 years. ...
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