Question

Find the probability function corresponding to the random variable x when a coin is tossed twice: assuming that the coins is fair?

Answer 1

Answer on Question #62598 – Math – Statistics and Probability

Question

Find the probability function corresponding to the random variable $X$ when a coin is tossed twice: assuming that the coin is fair?

Solution

If a coin is tossed twice, then the sample space is $S = \{HH, HT, TH, TT\}$, where $H$ and $T$ mean head and tail respectively. Let $X$ represent the number of heads that may come up. Hence $X$ is the random variable that takes the value 0, 1, and 2. Assuming that the coin is fair, we have

$$P(X = 0) = P(\{TT\}) = \frac{1}{4}$$ $$P(X = 1) = P(\{HT\}) + P(\{TH\}) = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}$$ $$P(X = 2) = P(\{HH\}) = \frac{1}{4}$$

Thus, the probability mass function is given by

$$p_X(0) = \frac{1}{4}, \quad p_X(1) = \frac{1}{2}, \quad p_X(2) = \frac{1}{4},$$

or it is given by the next table:

Let the random variable $Y$ represent the number of tails that may come up. It should be noted that the random variable $Y$ has the same probability mass function.

Answer:

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