Probability

Discrete Random Variables

Discrete Random Variables - Cumulative Distribution Function

         

If the cumulative distribution function of a discrete random variable X X which takes on integer values is given by FX(x)={0(x<0)cx(0x<12)1(x12), 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)? P(X = 7)?

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

If the cumulative distribution function of a discrete random variable X X which takes on integer values is FX(x)={0(x<0)1102(x2+20x)(0x<10)1(x10), 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)? P(X = 4)?

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

If the cumulative distribution function of a discrete random variable X X which takes on integer values is FX(x)={0(x<0)x2100(0x<10)1(x10), 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(X4)? P( X \ge 4)?

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

If the cumulative distribution function of a discrete random variable X X which takes on integer values is given by FX(x)={0(x11)1(x12), F_X(x) = \begin{cases} 0 \quad (x\le 11) \\ 1 \quad (x \ge 12), \end{cases} what is the probabilty P(X=14)? P(X = 14)?

If the cumulative distribution function of a discrete random variable X X which takes on integer values is FX(x)={0(x<0)x2144(0x<12)1(x12) 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]? E[X]?

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

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