Question

Consider tossing 4 coins, which are properly balanced so that the probability of a head at each toss is p= 1/2. Let r be the number of heads resulting from the 4 tosses.
Construct the probability distribution for r. (4 Marks)
Compute the expected value and variance for r. (2

Answer 1

Tossing a fair coin has two outcomes, Head or Tail. Thus, tossing a coin more than once has a binomial distribution with P=0.5. Probability distribution of tossing a fair coin four times is

$\binom{4}{r}0.5^r0.5^{4-r},r=0,1,2,3,4$

Where r is the number of heads

$\binom{4}{r}0.5^4,r=0,1,2,3,4$

$E(r)=np=4×0.5=2$

$Var(r)=4×0.5×0.5=1$