Probability Theory - Conditional Distributions and Independence

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 9 x - 11 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$ .

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 6 x - 10 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$ .

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 10 x - 10 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 10 x - 13 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 7 x - 14 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$ .

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$ .

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - 19 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 5 x - 6 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$ .

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- 9 x - 12 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Let $\uptext{X}$ , and $\uptext{Y}$ be the lifespans (in hours) of two electronic devices, and their joint probability mass function is given below.

$\operatorname{f_{X,Y}}{\left (x,y \right )} = \begin{cases} c e^{- x - 2 y} & 0<x<y<\infty \ 0, & \text{Otherwise} \end{cases}$

Determine the value of $\uptext{c}$

Conditional Distributions and Independence