Question

6.12.

Use R to pick 5 cards from a deck of 52. Did you get a pair or better? Repeat until you do. How long did it take?

6.9.

How much area is to the right of 1.5 for a normal (0,2)?

Solve using R software

Answer 1

Part 6.12

First we create a vector in R that resembles a deck of 52 cards.

R-code:

suits <- rep(c("Club", "Spade", "Diamond", "Hearts"),each=13)
value <- rep(c("Ace", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten", "Jack", "Queen", "King"),times=4)
cards <- paste(value,"of",suits)

An example value of 'cards' vector is "Queen of Hearts"

Now we will use the 'sample' function in R to simulate a sample draw. We say it is a pair, when two same value come up in the sample. We use the sample function without replacement option.

R-code:

sample(cards, size = 5,replace = FALSE)

For my simulation it took 2 tries for me to get a pair.

Part 6.9:

Let us say X is a random variable, such that

Area to the right of 1.5 means, we have to find

Using 'pnorm' function of R, we get

R-Code:

pnorm(1.5, mean=0, sd=2,lower.tail=F)

So the area to right of 1.5 for a N(0,2) is 0.2266274.