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We have a coin that we throw twice. If $X$ is the random variable that represent the number of heads.

I want to find the distribution function $F_X(x)$ in the intervals $0

The results of the coin are the following:

  • TT
  • TH
  • HT
  • HH

How could we calculate $F_X(x)$ at each interval?

1 Answers 1

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$X$ is discrete, we have $X=0,1$ or $2$.

By definition, $$F_X(x)=P(X \leq x)$$ if $x<0$, $P(X \leq x)=0$ because $X$ cannot be strictly negative.

if $0 \le x <1$, $P(X \leq x)$ is the probability that $X=0$, which is $\frac{1}{4}$

if $1 \le x <2$, $P(X \leq x)$ is the probability that $X=1$ or $X=0$, which is $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$

  • 0
    Ahh ok!! If we have the interval $x\geq 2$, we have that $P(X\leq x)$ is the probability $X=0$ or $X=1$ or $X=2$, so $\frac{1}{4}+\frac{1}{2}+\frac{1}{4}=1$, right? – 2017-02-02
  • 0
    That's correct ! – 2017-02-02
  • 0
    Great!! Thank you!! :-) – 2017-02-02