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 If these letters are withdrawn then it gets replaced.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.
Write down the sample space for X variable.
Can we write the sample space as given below:
S = {1, 2 and 3}.
No, the sample space cannot be written as S = {1, 2 and 3}.
The sample space is the set of all possible outcomes of a random experiment. In this case, the random experiment is withdrawing a letter from the hat.
The word "YACHT" has 5 letters. When any one of these letters is chosen, it can be either a vowel (A or E) or a consonant (Y, C, H, or T). For each letter, there are three possible outcomes: 1 (vowel), 2 (consonant), or 3 (other letter).
As a result, the sample space for X variable can be written as S = {1, 2, 3, 1, 2}, where each number corresponds to the outcome of withdrawing each letter in the word "YACHT".