Question 1027798
Q1 
Suppose that the random variable X has the following cumulative distribution function:
x	-1	1	3	5
F(x)	1/4	1/2	3/4	1 
Find the probability distribution of this random variable.
Find p(x<3),p(x &#8805;1 ) 
Find the mean of the random variable X.
Find the standard deviation of the random variable X. 

The pdf should be as follows:
x	-1	1	3	5
p(x)	1/4	1/4	1/4	1/4 
Hence it is discrete uniformly distributed.
p(x<3) = p(-1) + p(1) = 1/2, as can be directly read off from the table for F(x).
p(x &#8805;1) = 1 - 1/4 = 3/4, as can be read off again from the table for F(x).
Mean is {{{E(X) = (-1+1+3+5)*(1/4) = 2}}}.
Variance is {{{Var(X) = E(X^2) - (E(X))^2 = ((-1)^2+1^2+3^2+5^2)*(1/4) - 2^2 = 36/4 - 4 = 9-4 = 5}}}
==> {{{SD(X) = sqrt(5) = 2.236}}} approximately