Mathematics, 02.07.2020 22:01 ARandomPersonOnline
A point is chosen at random inside a triangle with vertices at (0, 0), (0, 8), and (8, 0). The continuous random variable denotes the x-coordinate of that point.
a) Find the probability that is less than 5.
b) Find the cumulative distribution function (i. e. P( ≤ x) ).
c) Find the probability density function.
d) Find the average value of X.
Answers: 2
are uniformly distributed, we have the joint density
is the area of the triangle 
is the portion of 
is between 0 and 5)
for some 
between 0 and 8)
is
![E[X]=\displaystyle\int_0^8xf_X(x)\,\mathrm dx](/tpl/images/0700/1108/9a010.png)
![E[X]=\displaystyle\frac1{32}\int_0^8x(8-x)\,\mathrm dx=\boxed{\frac83}](/tpl/images/0700/1108/5f6f2.png)
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A point is chosen at random inside a triangle with vertices at (0, 0), (0, 8), and (8, 0). The conti...
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