Question

constructing a probability distribution
coin toss
heads: x probability: $p_x(x)$
0 $a$
1 $b$
2 $c$
a coin is tossed two times. the set of outcomes is given as $s = \\{hh, ht, th, tt\\}$.
let $x$ represent the number of times heads occurs.
complete the table.
$a = \square$
$b = \square$
$c = \square$

Explanation:

Step1: Find \( a \) (X=0)

When \( X = 0 \), it means no heads. The outcome is \( TT \). There is 1 such outcome. Total outcomes: 4. So \( a=\frac{1}{4}=0.25 \).

Step2: Find \( b \) (X=1)

When \( X = 1 \), heads occur once. Outcomes: \( HT, TH \). There are 2 such outcomes. So \( b=\frac{2}{4}=0.5 \).

Step3: Find \( c \) (X=2)

When \( X = 2 \), heads occur twice. Outcome: \( HH \). There is 1 such outcome. So \( c=\frac{1}{4}=0.25 \).

Answer:

\( a = 0.25 \)
\( b = 0.5 \)
\( c = 0.25 \)