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.