Consider the experiment of tossing three fair coins and Let X denote the total n

Question

Consider the experiment of tossing three fair coins and Let X denote the total number of heads observed. (a) Is X a random variable? Explain why. (b) How many possible values can X assume? (c) Identify all the possible values of X. (d) Is X a discrete random variable? Explain why. (e) Represent the distribution of X as a table by referring to page 20 of Lecture Note #12 (Note that the example on page 20 only has 2 coins, not 3 coins). Fill all the blanks in the table. (f) Use the table method to calculate the expected value mu. (g) Use the table method to calculate the variance sigma^2. (h) Calculate sigma.

Explanation / Answer

a) X denotes the total number of heads in 3 coin tossse. Therefore it is a random variable as random variable is a process of choosing a random number which is a case here as we will see that X can take values : 0,1,2,3 all with some distinct probabilities.

b) X can have 4 possible values that is there could be 0,1,2, or 3 heads in 3 tosses.

c) All possible values of X are :0,1,2,3

d) X is a discrete random variable because it can only take discrete values on the number line : 0,1,2 and 3 in this case.

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