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. Is X a random variable? Explain why. How many possible values can X assume? Identify all the possible values of X. Is X a discrete random variable? Explain why. 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. Use the table method to calculate the expected value mu. Use the table method to calculate the variance theta^2. Calculate theta.

Explanation / Answer

A) X is a random variable as X can take any value from 0 to 3 randonly

B) There are 4 possible values

C) possible values of x are 0, 1, 2 and 3

D) X is a discrete random variable as X cannot be any value in between 1 or 2, 2 or 3 etc. The number of values x can have is fixed

E)

f) mean = sum of xf(x)

=0+ 1x3/8 + 2x3/8 + 3x1/8 = 1.5

g) variance = sum of [(x-mean)2f(x)]

= (-1.5)2x(1/8) + (1-1.5)2x3/8 + (2-1.5)2x3/8 + (3-1.5)2x1/8

= 0.75

h) standard deviation = square root of variance = 0.866

X 0 1 2 3 P(x) 1/8 3/8 3/8 1/8

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