SOLUTION: 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 var

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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 ≥1 )
Find the mean of the random variable X.
Find the standard deviation of the random variable X.



Q2


The cumulative distribution function of the random variable X is given by:
F(x)={0(1- 9/x^2 ) for3 Find the probability density function for the random variable X.
compute p(X≤ 5) and p( 8< X )
Find the expected value for the random variable X.



Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
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 ≥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 ≥1) = 1 - 1/4 = 3/4, as can be read off again from the table for F(x).
Mean is E%28X%29+=+%28-1%2B1%2B3%2B5%29%2A%281%2F4%29+=+2.
Variance is
==> SD%28X%29+=+sqrt%285%29+=+2.236 approximately