Question

In 10 tosses of seven coins, the numbers of heads were 2, 6, 2, 2, 5, 3, 5, 3, 3, 4. If the observations are denoted by Y1, Y2, Yn:

a. What is the value of n?
b. What is the value of Y2?
c. What is the value of Y7?
d. For what values of i does Y = 2? 3? 4?
e. Distinguish between Yi-1 and Yi – 1.
f. What do Yi-1 and Yi – 1 equal for i = 2?
g. Write the observations as a vector.

Answer 1

Answer: a. The value of n is 10, as there are 10 tosses of seven coins.

b. The value of Y2 is 6, as the number of heads in the second toss is 6.

c. The value of Y7 is 3, as the number of heads in the seventh toss is 3.

d. For i = 1, 2, 3, 4, the value of Y is 2. For i = 5, 8, the value of Y is 3. For i = 6, 9, 10, the value of Y is 4.

e. Yi-1 refers to the observation made in the previous toss (i-1), whereas Yi – 1 refers to the observation made in the current toss (i) minus 1.

f. Yi-1 = Y1 = 2 and Yi – 1 = Y2 – 1 = 6 – 1 = 5 for i = 2

g. The observations can be written as a vector Y = (2, 6, 2, 2, 5, 3, 5, 3, 3, 4)

Explanation: