Question

Given the possible outcomes of the probability experiment, tossing four unbiased coin simultaneously. Construct the probability distribution where random variable x refers to the number of heads.

Answer 1

It's the binomial distribution:

$n=4, \space \space p = q = \cfrac{1}{2}$

$Pr(x=k)= \binom{4}{k} (\cfrac{1}{2})^{k} \cdot(1-\cfrac{1}{2})^{4-k}=\binom{4}{k} (\cfrac{1}{2})^{4}=\binom{4}{k} (\cfrac{1}{16})$ where $k$ denotes number of heads.

Thus:

$Pr(x=0)= \binom{4}{0} (\cfrac{1}{16}) = \cfrac{1}{16}$

$Pr(x=1)= \binom{4}{1} (\cfrac{1}{16}) = \cfrac{4}{16}$

$Pr(x=2)= \binom{4}{2} (\cfrac{1}{16}) = \cfrac{6}{16}$

$Pr(x=3)= \binom{4}{3} (\cfrac{1}{16}) = \cfrac{4}{16}$

$Pr(x=4)= \binom{4}{4} (\cfrac{1}{16}) = \cfrac{1}{16}$