Suppose that you choose a letter at random from the word sta

Suppose that you choose a letter at random from the word “statistics? and that you continue to choose letters at random (without replacement) until you select a vowel. Let the random variable Y represent the number of letters that you choose in order to get a vowel.

(a) Determine the probability distribution of Y .

(b) Repeat part (a) in the case that the sampling is performed with replacement.

Solution

Here total alphabets =10 , among them vowels 3 and the remaining 7 are consonants.

The probability distribution of Y is

b) In the case of replacement, probability of a getting a vowel =3/10

probability of not getting a vowel = 7/10

Let \'Y\' be the number of letters that you choose in order to get vowel is

P(Y=y) =(0.7)^y-1 * (0.3)