Lesson test: Variance and spread

1.[2p]
Why is $E [X - μ]$ useless as a measure of spread?

It is zero for every random variable, since deviations above and below cancel

Correct

It is negative whenever the distribution is skewed

The answer is: It is zero for every random variable, since deviations above and below cancel

It has the wrong units

The answer is: It is zero for every random variable, since deviations above and below cancel

It cannot be computed without knowing the sample space

The answer is: It is zero for every random variable, since deviations above and below cancel

4.[3p]
Two fair dice are rolled independently. What is the standard deviation of the total? Give the answer to four decimal places.

CorrectNot quite: 2.4152

5.[2p]
If $operatorname {C o v} (X, Y) = 0$ then $X$ and $Y$ are independent.

True

The answer is: False

False

Correct

6.[3p]
A measurement has standard deviation $0.8$ grams. How many independent repeats are needed for the average to have standard deviation $0.1$ grams?

CorrectNot quite: 64

7.[3p]
Why did Kerrich's surplus of heads grow while his fraction of heads converged?

The count has standard deviation $\sqrt{n} / 2$ , which grows, while the fraction has $1 / (2 \sqrt{n})$ , which shrinks

Correct

The coin was slightly biased towards heads

The answer is: The count has standard deviation $\sqrt{n}/2$, which grows, while the fraction has $1/(2\sqrt{n})$, which shrinks

The tosses were not independent

The answer is: The count has standard deviation $\sqrt{n}/2$, which grows, while the fraction has $1/(2\sqrt{n})$, which shrinks

The two columns cannot both be right

The answer is: The count has standard deviation $\sqrt{n}/2$, which grows, while the fraction has $1/(2\sqrt{n})$, which shrinks

8.[2p]
Chebyshev's inequality bounds the probability of being at least $2.5$ standard deviations from the mean. What is that bound?

CorrectNot quite: 0.16

9.[3p]
Which of these are true of Chebyshev's inequality?

Select all that apply

It holds for any distribution with a finite variance

Correct

It is usually far looser than the true probability

Correct

It requires the distribution to be symmetric

The answer is: It holds for any distribution with a finite variance, It is usually far looser than the true probability

It requires the distribution to be bell shaped

The answer is: It holds for any distribution with a finite variance, It is usually far looser than the true probability

Sign in

Variance and spread

1.[2p]
Why is $E [X - μ]$ useless as a measure of spread?

2.[2p]
For one roll of a fair die, what is the variance? Give the answer to four decimal places.

3.[2p]
A variable has variance $9$ . What is the variance of $5 X + 2$ ?

4.[3p]
Two fair dice are rolled independently. What is the standard deviation of the total? Give the answer to four decimal places.

5.[2p]
If $operatorname {C o v} (X, Y) = 0$ then $X$ and $Y$ are independent.

6.[3p]
A measurement has standard deviation $0.8$ grams. How many independent repeats are needed for the average to have standard deviation $0.1$ grams?

7.[3p]
Why did Kerrich's surplus of heads grow while his fraction of heads converged?

8.[2p]
Chebyshev's inequality bounds the probability of being at least $2.5$ standard deviations from the mean. What is that bound?

9.[3p]
Which of these are true of Chebyshev's inequality?

1.[2p] Why is E[X-μ] useless as a measure of spread?

2.[2p] For one roll of a fair die, what is the variance? Give the answer to four decimal places.

3.[2p] A variable has variance 9. What is the variance of 5X+2?

4.[3p] Two fair dice are rolled independently. What is the standard deviation of the total? Give the answer to four decimal places.

5.[2p] If operatorname{Cov}(X,Y)=0 then X and Y are independent.

6.[3p] A measurement has standard deviation 0.8 grams. How many independent repeats are needed for the average to have standard deviation 0.1 grams?

7.[3p] Why did Kerrich's surplus of heads grow while his fraction of heads converged?

8.[2p] Chebyshev's inequality bounds the probability of being at least 2.5 standard deviations from the mean. What is that bound?

9.[3p] Which of these are true of Chebyshev's inequality?

1.[2p]
Why is $E [X - μ]$ useless as a measure of spread?

2.[2p]
For one roll of a fair die, what is the variance? Give the answer to four decimal places.

3.[2p]
A variable has variance $9$ . What is the variance of $5 X + 2$ ?

4.[3p]
Two fair dice are rolled independently. What is the standard deviation of the total? Give the answer to four decimal places.

5.[2p]
If $operatorname {C o v} (X, Y) = 0$ then $X$ and $Y$ are independent.

6.[3p]
A measurement has standard deviation $0.8$ grams. How many independent repeats are needed for the average to have standard deviation $0.1$ grams?

7.[3p]
Why did Kerrich's surplus of heads grow while his fraction of heads converged?

8.[2p]
Chebyshev's inequality bounds the probability of being at least $2.5$ standard deviations from the mean. What is that bound?

9.[3p]
Which of these are true of Chebyshev's inequality?