I am tackling the question below:
f(x)=(2x^2+3)/75, x≥0
g(x)=|3x-4|/10,x belongs to R
After the two functions, there are several questions that I can solve, but then comes a new situation which combines with probability distribution.
The domains of f and g are now restricted to {0,1,2,3,4}
(D)byconsidering the values of f and g on this new domain, determine which of f and g could be used to find a probability distribution for a discrete random variable X, stating your reasons clearly
(E)Using this probability distribution, calculate the mean of X
I’ve just learnt various of distribution and I felt really confused on the concepts! Can anyone provide some ideas???
Hints:
D) One property of a discrete probability distribution is that $\sum\limits_{x\in D} f(x)=1$, where D is the range of the discrete random variable $x$.
E) The mean is defined as $\mu=\sum\limits_{x\in D} x\cdot f(x)$
To get the mean of the $f(x)$ you have to calculate $\sum\limits_{x=0}^4 x\cdot \frac{2x^2+3}{75}$