Question

Let X be an exponential random variable with parameter 2. Find the CDF of X . Express your answer in terms of x using standard notation. Use 'e' for the base of the natural logarithm (e.g., enter e^(-3*x) for e−3x ). a) For x≤0 , FX(x)= unanswered b) For x>0 , FX(x)=

Answer 1

Answer:

$F(x,\lambda) = 1-e^{2x}$     for      $x\geq0$

and   $F(x,\lambda) = 0$    for   $x$

Step-by-step explanation:

Remember that the CDF of an exponental random variable is given by

$F(x,\lambda) = \left \{ {{1-e^{\lambda x} \ \ \ \ \ x\geq 0} \atop {0} \ \ \ \ \ \ \ \ \ \ \ x$

where   $\lambda$   is the parameter.  In this case    $\lambda = 2$  so, for this case

$F(x,\lambda) = \left \{ {{1-e^{2x} \ \ \ \ \ x\geq 0} \atop {0} \ \ \ \ \ \ \ \ \ \ \ x$