Probability Weibull Distribution

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Homework Statement

Suppose that x has a Weibull distribution with parameters $\alpha$ and $\beta$ and that $P(x \leq 1)=.105$ and $P(2 \leq x)=.641$. What are $\alpha$ and $\beta$?

Homework Equations

$F(x) = 1 - e^{-(\frac{x}{\beta})^{\alpha}}$

The Attempt at a Solution

When I try and solve I get

$ln(.641) = -(\frac{1}{\beta})^{\alpha}$
$ln(.895) = -(\frac{1}{\beta})^{\alpha}$

This is a problem. I don't see how else to solve this problem.

.105 = F(1) - F(0)
.641 = 1- [F(2) - F(0)]

Thanks for any help.

 

[Ray Vickson]

Homework Statement

Suppose that x has a Weibull distribution with parameters $\alpha$ and $\beta$ and that $P(x \leq 1)=.105$ and $P(2 \leq x)=.641$. What are $\alpha$ and $\beta$?

Homework Equations

$F(x) = 1 - e^{-(\frac{x}{\beta})^{\alpha}}$

The Attempt at a Solution

When I try and solve I get

$ln(.641) = -(\frac{1}{\beta})^{\alpha}$
$ln(.895) = -(\frac{1}{\beta})^{\alpha}$

This is a problem. I don't see how else to solve this problem.

.105 = F(1) - F(0)
.641 = 1- [F(2) - F(0)]

Thanks for any help.

Do you know what F(x) is actually supposed to represent? How would that relate to the given data? In particular, what are the values of x for your given data?

Note: to avoid confusion, make a distinction between X (a random variable) and x (a possible numerical value of X). These are NOT the same. So, your given data are
$$P(X \leq 1) = 0.105 \;\text{ and } P(2 \leq X) = P(X \geq 2) = 0.641.$$