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 If these letters are withdrawn then it gets replaced.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.

Which value should be assigned to the letter “Y” since it can be a vowel or consonant?

Write down the sample space for X variable.

Since "Y" can be either, I would assign it to "all other retrieved letters."

Thank you PsyDAG.

Can we write the sample space as given below:

S = {Y3, A1, C2, H2 and T2}.

To determine which value should be assigned to the letter "Y," we need to consider whether "Y" is more commonly used as a vowel or as a consonant in the English language.

The majority of the time, "Y" is used as a consonant at the beginning of a word (e.g., "yellow") or when it represents a sound other than the vowel sounds "a," "e," "i," "o," or "u" (e.g., "system"). However, "Y" can function as a vowel in some cases, such as when it represents the "ee" sound (e.g., "happy") or when it replaces an "i" in certain words (e.g., "myth").

Since "Y" can be both a vowel and a consonant, we need to assign the appropriate value based on how it is used in the word "YACHT." In this word, "Y" functions as a consonant because it represents the "y" sound at the beginning of the word. Therefore, in this specific case, the value assigned to the letter "Y" should be 2.

Now, let's write down the sample space for the random variable X. The sample space is the set of all possible outcomes for the variable X. In this scenario, the sample space for X would consist of all the letters in the word "YACHT." Since the letters are replaced after each withdrawal, the sample space would be:

{Y, A, C, H, T}