A box is to be constructed so that its heights is 10 inches and its base is X inches by X inches. Suppose that X has a continuous uniform distribution on the interval [8,11].
What is the probability density function of the random variable X?
Express the volume V of the box as a functio of X, and determine the expected volume of the box in cubic inches?
Just help me if you know ANYTHING
2007-11-17 06:58:41 · 1 answers · asked by Lin-z 2 in Science & Mathematics ➔ Mathematics
please help.. i dont know how to express the volume as a function of x and determine the expected volume of the box in cubic inches.. after this im supposed to find the probability that the volume of the box is no greater than 1000 inches?
2007-11-17 09:36:11 · update #1
Volume of a box is Length times Width times Height
In this case, the length and width are equal and both written as X. So the volume V is given by 10X²
I'm sure you can find the probability density function f(x) of the random variable X, if X has a continuous uniform distribution on the interval [8,11]. If the box is a distraction, forget about it for the moment.
Then the expected volume of the box is E[10X²] = 10E[X²] = 10*integral from 8 to 11 of x² f(x) dx
You should get 910 cubic inches.
2007-11-17 10:21:15 · answer #1 · answered by Ron W 7 · 0⤊ 0⤋