Answer to Question #140636 in Statistics and Probability for George Chola

Question

Qn.3 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.
REQUIRED:
i.) Construct the probability distribution for r. (4 Marks)
ii.) Compute the expected value and variance for r. (2 Marks

Answer 1

$r \sim Binomial(n, P) \\ r \sim Binomial(4,0.5) \\ I) P(r)=C_{r}^{4}( 0.5)^r (0.5)^{4-r}\\ =C_{r}^{4}(0.5)^{4} \\ II) E(r) =np=4(0.5)=2\\ V (r) =np(1-p)=4(0.5)(0.5)=1$