Answer to Question #236591 in Statistics and Probability for john k

Question

In an introductory statistics class of 50 students, there are 11 freshman, 19 sophomores, 14 juniors and 6 seniors. One student is selected at random. What is the sample space of this experiment? Construct a random variable X for this sample space and then find its space. Further, find the probability density function of this random variable X.

Answer 1

The sample space of this experiment is

$$S=\{freshman, sophomore, junior,senior\}$$

Let the random variable $X$ be the number of juniors in the sample

$$X=\{0,1\}$$

The probability density function is

$$p_X(x)= \begin{cases} 36/50,&x=0 \\ 14/50, &x=1 \\ 0, & otherwise \end{cases}$$

Or

$$p_X(x)= \begin{cases} 0.72,&x=0 \\ 0.28, &x=1 \\ 0, & otherwise \end{cases}$$