R Exercises

Sampling Letters

The built$-$in vector letters contains the $26$ lower$-$case letters of the alphabet.

a$.$ Using the sample$()$ function, take a sample of $10$ letters without replacement from letters $.$

b$.$ Using the $`$ sample$()$ function, take a sample of $10$ letters with replacement from letters $.$

Sampling Letters $($continued$)$

a$.$ Write a function to take a sample of $10$ letters without replacement from letters $.$

b$.$ Add a line in the function so that the function returns the number of vowels in the sample. $($If the sample is stored in

the vector $y,$ then the line of code

sum$($y $\%$in$\%$ c$("$a$","$e$","$i$","$o$","$u$"))$

will count the number of vowels in the sample.$)($c$)$ Using the function replicate$(),$ take $50$ samples, storing the

number of vowels from the samples in the vector $n_{-}$vowels $.($d$)$ Approximate the probability that there are two vowels in

your sample.