Question

X, is assumed to be a random variable by placing letters of the word “YACHT” in a hat. If these letters are withdrawn then it gets replaced. A value of 1 is given when a vowel is retrieved, and a value of 2 is given when a consonant is retrieved while a value of 3 is given to all other retrieved letters.

Question: Write down the sample space on which X variable is defined.

Can we write the sample space as given below:

Since Y-2, A-1, C-2, H-2, T-2

Sample space = {1 and 2}.

Is there another way of writing this as required in the question?

Answer 1

I have seen this question for several days now.
More than likely, the reason you are not getting a reply is due to your notation.
Secondly, I am baffled by your choices.
- for a vowel , use a value of 1
- for a consonant, use a value of 2
- "other retrieved letters" , a value of 3

In my alphabet there are only vowels and consonants.

Answer 2

But this was the question given to us.

I believe there are specific values 1-3 assigned in order to construct a discrete probability distribution for X variable.

Anyway, do you think the sample space seems to be alright?

Answer 3

As I said, I am not familiar with your notation.

counting Y as a vowel,
Prob(vowel) = 1/5
Prob(consonant) = 4/5

Answer 4

I think you meant:

Counting "A" as a vowel

P (vowel) = 1/5.

Answer 5

the vowel/consonant ambiguity of "Y" is probably an issue here