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Probability

Discrete Random Variables

Concept Quizzes

Discrete Random Variables - Probability Density Function (PDF)
Discrete Random Variables - Cumulative Distribution Function
Discrete Random Variables - Joint Probability Distribution
Discrete Random Variables - Problem Solving
Discrete Random Variables - Indicator 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 $x.$

\frac{1}{11}

\frac{2}{11}

0

\frac{1}{12}

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by Brilliant Staff

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 $x.$

\frac{19}{100}

\frac{21}{100}

\frac{3}{20}

\frac{13}{100}

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by Brilliant Staff

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 $x.$

\frac{3}{100}

\frac{91}{100}

\frac{3}{10}

\frac{9}{100}

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by Brilliant Staff

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 $P(X = 14)?$

\frac{1}{14}

\frac{1}{12}

\frac{6}{7}

0

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by Brilliant Staff

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 $x.$

13

\frac{1001}{24}

\frac{2041}{24}

\frac{611}{72}

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by Brilliant Staff