The probability distribution function : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- Explain why $\lim_{x\rightarrow -\infty} F_X(x)=0$ $F_X(x)$ is the probability distribution function for the random variable $X$
- Explain why $\lim_{x\rightarrow +\infty} F_X(x)=1$. $F_X(x)$ is the probability distribution function for the random variable $X$
- Consider a die and explain what set of outcomes are in each of the following subsets $\{ s : (s \in \Omega ) \wedge (x(s) \le 0 \}$, $\{ s : (s \in \Omega ) \wedge (x(s) \le 1 \}$, $\{ s : (s \in \Omega ) \wedge (x(s) \le 1.5 \}$, $\{ s : (s \in \Omega ) \wedge (x(s) \le 4.5 \}$ and $\{ s : (s \in \Omega ) \wedge (x(s) \le 6.25 \}$. In these expressions $\Omega$ is used to represent the sample space for the experiment and $x(s)$ tells you the value that comes up when the dice is rolled.
- Sketch the probability distribution function for a random variable $X$ tells you the outcome of a fair dice roll. Indicate all the points on this curve where the function is discontinuous.
- Write a mathematical expression using limits which tells us that the function $f(x)$ has a discontinuity at $a$.
- Explain why $\lim_{x\rightarrow -\infty} F_X(x)=0$ $F_X(x)$ is the probability distribution function for the random variable $X$
- Explain why $\lim_{x\rightarrow +\infty} F_X(x)=1$. $F_X(x)$ is the probability distribution function for the random variable $X$
- Consider a die and explain what set of outcomes are in each of the following subsets $\{ s : (s \in \Omega ) \wedge (x(s) \le 0 \}$, $\{ s : (s \in \Omega ) \wedge (x(s) \le 1 \}$, $\{ s : (s \in \Omega ) \wedge (x(s) \le 1.5 \}$, $\{ s : (s \in \Omega ) \wedge (x(s) \le 4.5 \}$ and $\{ s : (s \in \Omega ) \wedge (x(s) \le 6.25 \}$. In these expressions $\Omega$ is used to represent the sample space for the experiment and $x(s)$ tells you the value that comes up when the dice is rolled.
- Sketch the probability distribution function for a random variable $X$ tells you the outcome of a fair dice roll. Indicate all the points on this curve where the function is discontinuous.
- Write a mathematical expression using limits which tells us that the function $f(x)$ has a discontinuity at $a$.