In the experiment of tossing two fair coins, let $X$ be the number of heads. Then the probability distribution of $X$ is:
A$P[X=0]=0, P[X=1]=1/2, P[X=2]=1/2$
B$P[X=0]=1/4, P[X=1]=1/4, P[X=2]=1/2$
C$P[X=0]=1/2, P[X=1]=1/4, P[X=2]=1/4$
D$P[X=0]=1/4, P[X=1]=1/2, P[X=2]=1/4$
Answer & Solution
Correct answer: D. $P[X=0]=1/4, P[X=1]=1/2, P[X=2]=1/4$
Sample space {HH, HT, TH, TT}. $X=0$: TT → 1/4. $X=1$: {HT, TH} → 2/4 = 1/2. $X=2$: HH → 1/4. Sum = 1 ✓.
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