Help Understanding this Integral: int_{1,t} [1/(theta - 1)] dy = (t - 1)/(theta - 1)

[warmtomatoes]

Can someone please explain this answer? This is part of a mathematical statistics question, but my calculus is not very good.

$$\int_1^t \frac{1}{\theta - 1}dy = \frac{t-1}{\theta-1}$$
The full problem and solution are attached. (The MLE for theta is Y(n).)

 

[Dr.Peterson]

Can someone please explain this answer? This is part of a mathematical statistics question, but my calculus is not very good.

$$\int_1^t \frac{1}{\theta - 1}dy = \frac{t-1}{\theta-1}$$
The full problem and solution are attached. (The MLE for theta is Y(n).)

Since $\theta$ is just a constant, as far as y is concerned, you can pull $\frac{1}{\theta-1}$ outside of the integral. The integral of 1 dy is y, and so on.

 

[Steven G]

Hint: $\displaystyle \int_1^t dy = y |_1^t = t-1$

 

[nasi112]

Let $\displaystyle 5 = \frac{1}{\theta - 1}$

Now imagine you have this integral $\displaystyle \int_{1}^{t} 5 \ dy.$ How would you solve it?