Flipping a biased coin

Question

A biased coin with a probability of 0.7 of landing on heads is flipped 100 times. Let X represent # of heads. Calculate the following

a) E[X]

b) Var(X)

c) Median of X

d) Prob. of getting at least 15 heads in a row

Answer 1

n = 100 coin tosses

p = probability of getting heads

Expected Value (Mean): E[X] = np = (100)(0.7) = 70

Variance: Var[X] = np(1-p) = (100)(0.7)(0.3) = 21

Median of X is 70. However, we don't know if the binomial distribution is symmetrical (bell-shaped curve).

This tells you that in about 50% of all cases you will have less than 70 heads, and in the other ~50% of the cases you have 70 or more heads.

100

P(X ≥ 15): ∑_x=15 (100 choose x) (0.7)^x (0.3) ^100-x