Answer to Question #292281 in Statistics and Probability for Yaku

Question

1. For each of the following, determine whether it can serve as the probability distribution of some random variable:

a) p(k) = 1/7 , for k = 0; 1; 2; 3; 4; 5;

b) p(x) = x² /30 , for x = 0; 1; 2; 3; 4;

c) p(y) = (y+4)/(y-4) , for y = 1; 2; 3; 4; 5.

2. Suppose that a random variable X can only take on values on the continuous interval from 0 to 4, and that its probability density function is given by:

f(x) =x/8; for 0 \legslant  x \legslant 4:

a) Draw a graph of the probability density function.

b) Proof that it is a proper density function.

c) What is the probability that X will take on a value less than 2?

d) What is the probability that X will take on a value greater than 3?

e) What is the probablity that X will take on a value between 1 and 2.5? [Answer parts ( b) to (e) without doing any integration]

3. For Exercise 2 above, determine the mean and standard

deviation. Locate the mean on your graph in Exercise 2.