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 If these letters are withdrawn then it gets replaced.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?
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.
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?
As I said, I am not familiar with your notation.
counting Y as a vowel,
Prob(vowel) = 1/5
Prob(consonant) = 4/5
I think you meant:
Counting "A" as a vowel
P (vowel) = 1/5.
the vowel/consonant ambiguity of "Y" is probably an issue here
Yes, the sample space can be defined as the set of all possible outcomes or values that the random variable X can take on. In this case, X represents the value associated with the letters drawn from the hat.
To write the sample space, we can consider all the possible letters in the word "YACHT" and their associated values:
Y - 2 (consonant)
A - 1 (vowel)
C - 2 (consonant)
H - 2 (consonant)
T - 2 (consonant)
So the sample space can be written as: {2, 1, 2, 2, 2}.
Alternatively, you can write the sample space by grouping the values together based on their type:
Vowels (1): {1}
Consonants (2): {2, 2, 2, 2}
Other letters (3): {}
Therefore, the sample space can also be written as: {1, 2, 2, 2, 2}.