STAT 1030 Study Guide - Midterm Guide: Random Variable, Horse Length, South Dakota Highway 10

A  Compute and interpret the mean of the random variable x

B Compute the standard deviation of the random variable x.

C. What is the probability that a randomly selected student has a parent involved in three activities?

D  What is the probability that a randomly selected student has a parent involved in three or four activities?

E.

In the following probability distribution, the random variable x represents the number of activities a K to the 5th-grade student is involved in.

Complete parts (a) through (f) below.

   x           0              1               2               3               4

P(x)      0.299       0.145         0.234        0.053         0.269

(a) Verify that this a discrete probability distribution.

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space   Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

                                        Y=0                                Y=1

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?