Question

We have a red coin, for which P(Heads)=0.4, a green coin, for which P(Heads)=0.5 and a yellow coin for which P(Heads)=0.6. The flips of the same or of different coins are independent. For each of the following situations, determine whether the random variable N can be approximated by a normal. If yes, enter the mean and variance of N. If not, enter 0 in both of the corresponding answer boxes.

1. Let N be the number of Heads in 300 tosses of the red coin.

2. Let N be the number of Heads in 300 coin tosses. At each toss, one of the three coins is selected at random (either choice is equally likely), and independently from everything else.

3. Let N be the number of Heads in 100 tosses of the red coin followed by 100 tosses of the yellow coin (for a total of 300 tosses).

mean and variances ???

Answer 1

1. mean = 120, variance = 72

2. mean = 150, variance = 73

3. mean = 150, variance = 72

4. mean = 0, variance = 0

Answer 2

above answers are partially wrong

here right ones:

1. mean = 120, variance = 72

2. mean = 150, variance = 75

3. mean = 150, variance = 73

4. mean = 0, variance = 0