朋友的Rstudio作业，我完全不会，求各位大侠帮帮忙，可付费。

1. Suppose “Y1” is an object where > length(Y1) yields [1] 5 and > mean(Y1) yields [1] 5.4. Suppose
“Y2” is an object where > length(Y2) yields [1] 10 and > mean(Y2) yields [1] 8.3.
If we assign > Y3 = c(Y1, 3, Y2), then write the output for
(a) > length(Y3)
(b) > mean(Y3)
2. Attach the frequency histograms for ‘x4’ and ‘x4distr2’.
3. Of the 20,000 samples taken from ‘x4’, what is the mean of the 417 th sample? What is the confidence
interval based on the 417 th sample? What is the population mean of ‘x4’? Does that specific interval
actually contain the population mean of ‘x4’?
4. For the 20,000 confidence intervals for the samples from ‘x4’, about how many would you expect to contain
the mean of ‘x4’? Explain. How many of the intervals actually contain the mean? What code did you
type in to get this?
HINT: You might find the following code, that counts the number times the mean is less than the upper
bound, helpful to get you started on determining the relevant line of code:
> sum(x4ave < x4upper)
5. According to the Central Limit Theorem, what should the (theoretical) value of µ ¯ x equal for your specific
x4distr2 sampling distribution? Write an equation in terms of the object names used in this project. How
do your empirical results match the theoretical results of the theorem? That is, how does the actual value
of the µ ¯ x value for your x4distr2 compare to the theoretical value that it should be?
CU Boulder MATH 2510 - Introduction to Statistics 6
6. According to the Central Limit Theorem,what should the (theoretical) value of σ ¯ x equal for your specific
x4distr2 sampling distribution? Write an equation in terms of the object names used in this project. How
do your empirical results match the theoretical results of the theorem? That is, how does the actual value
of the σ ¯ x value for your x4distr2 compare to the theoretical value that it should be?
7. Determine which of the four probability functions {dbinom, pbinom, pnorm, qnorm} is most appropriate
to compute the answer to the following question. Then write the exact R-code that should be entered to
compute that answer, as well as the answer.
Denver Nuggets player Jamal Murray has a free throw percentage of 88.4% (we can say that the probability
that Jamal makes a single free throw is 88.4%). If Jamal attempts 30 free throws, what is the probability
that he makes at most 20 of them? Assume each free throw is independent of all others.
8. Using the while-loop provided in the quota problem in 5e as a guide, write the exact R-code that should
be entered to solve the following problem, as well as the answer.
The probability that a skeet shooter can hit 31 or more targets in 50 total shots is 0.35463. Find the
probability of this shooter hitting the target when he shoots at a single target. Provide an answer accurate
to 4 decimal places.
So, you know the cumulative probability P(r ≥ 31) = 0.35463. But, now determine the probability of
success on a single attempt using a while-loop.