Integrating factor question?
a. For what value of #\lambda# is the following ( #\int_1^2 \lamda\root(3)(x^4)dx# ) a density function?
b. Find #\mu#
Also: does anyone know where I can find practice questions on this type of problem?
a. For what value of
b. Find
Also: does anyone know where I can find practice questions on this type of problem?
1 Answer
See below
Explanation:
What you have here is a "wannabe" probability density function (PDF):
#mathbf P (x) = \lambda \ root(3)(x^4)# , for#1 le x le 2# .
But first you want to normalise the PDF, ie make this become true:
#int_1^2 mathbf P(x) = 1# .
....which is the continuous analogue of the requirement of a discrete distribution:
#sum_i P(x_i) = 1#
So:
And your PDF is:
The mean
#mu = int_1^2 x \ mathbb P(x) \ dx#
....which is the continuous analogue of the mean of a discrete distribution:
#mu = sum_i P(x_i) \ x_i#
Here: