Waste less time on Facebook — follow Brilliant.
×
Back to all chapters

Discrete Random Variables

How many heartbeats do you have each minute? How many points will your favorite team score in their game tonight? These any many other real-world values can be modeled by discrete random variables.

Discrete Random Variables - Cumulative Distribution Function

         

If the cumulative distribution function of a discrete random variable \( X \) which takes on integer values is given by \[ F_X(x) = \begin{cases} 0 \quad (x\lt 0) \\ c \left\lfloor x \right\rfloor \quad ( 0 \le x \lt 12 )\\ 1 \quad (x \ge 12), \end{cases} \] which of the following is an impossible value for the probabilty \( P(X = 7)? \)

Note: \( \left\lfloor x \right\rfloor \) refers to the greatest integer equal to or smaller than \(x. \)

If the cumulative distribution function of a discrete random variable \( X \) which takes on integer values is \[ F_X(x) = \begin{cases} 0 \quad (x\lt 0) \\ \frac{1}{10 ^{2}} \left( - \left\lfloor x \right\rfloor ^2 + 20 \left\lfloor x \right\rfloor \right) \quad ( 0 \le x \lt 10 )\\ 1 \quad (x \ge 10), \end{cases} \] what is the probabilty \( P(X = 4)? \)

Note: \( \left\lfloor x \right\rfloor \) refers to the largest integer not greater than \(x. \)

If the cumulative distribution function of a discrete random variable \( X \) which takes on integer values is \[ F_X(x) = \begin{cases} 0 \quad (x\lt 0) \\ \frac{\left\lfloor x \right\rfloor ^2}{100} \quad ( 0 \le x \lt 10 )\\ 1 \quad (x \ge 10), \end{cases} \] what is the probabilty \( P( X \ge 4)? \)

Note: \( \left\lfloor x \right\rfloor \) refers to the largest integer not greater than \(x. \)

If the cumulative distribution function of a discrete random variable \( X \) which takes on integer values is given by \[ F_X(x) = \begin{cases} 0 \quad (x\le 11) \\ 1 \quad (x \ge 12), \end{cases} \] what is the probabilty \( P(X = 14)? \)

If the cumulative distribution function of a discrete random variable \( X \) which takes on integer values is \[ F_X(x) = \begin{cases} 0 &\quad (x\lt 0) \\ \frac{\left\lfloor x \right\rfloor ^2}{144} &\quad ( 0 \le x \lt 12 )\\ 1 &\quad (x \ge 12) \end{cases} \] what is \( E[X]? \)

Note: \( \left\lfloor x \right\rfloor \) refers to the largest integer not greater than \(x. \)

×

Problem Loading...

Note Loading...

Set Loading...