Java Python STAT 312: Basic Statistics for Engineering and Science
Homework 2
See Canvas page ”Useful R functions for Statistics” for more information on functions like ppois() and qnorm().
You can find the data sets needed on the Canvas page ”Data sets for homework” .
1. (2 points) Let Y ~ Pois(4.5). Use the R function ppois() or dpois() to answer the following
(a) P (Y ≤ 7)
(b) P (2 ≤ Y < 6)
Note: ppois() is the cdf and dpois() is the pmf. Use help( STAT 312: Basic Statistics for Engineering and Science Homework 2R ppois) in R to learn more about these functions.
2. (3 points) Let Y ~ N (5, 32). Use the built-in R functions pnorm() and qnorm() to answer the following
(a) P (Y > 7.8)
(b) P (1.6 < Y ≤ 7.8)
(c) Find y that satisfies P (Y ≤ y) = 0.95
3. Exercise 6.5.4 a,b (4pt) Note: A time series plot is simply a scatterplot of a variable against time (e.g. year).
4. Exercise 6S16 a, b, and d (6pt)
5. Exercise 6.S18 a (2pt) and b (1pt)
6. (2 points) Use the built-in R functions rnorm() to simulate 10,000 random numbers from the N (1, 22) distribution. Don’t show the numbers(!) just store them in a variable, say x. Note: Use set.seed( . . .) so that you will get the same answers each time you generate the report (’knit’ the .Rmd file)
Calculate the mean and the standard deviation of your sample