1. Discrete Probility Distributions Questions. Assume X is a random variable.
(a) Values of a random variable, X, can not be negative or greater than one. (True or False)
(b) Probability that a random variable attains a particular value, P(X), can not be negative or greater than one. (True or False)
(c) If the sum of probability for all values random variable can attain is 1, then it doesn't matter the speci c values attained by P(X). (True or False)
(d) A probability distribution must have probability values which are non-negative and no larger than one, AND the sum of these probability values must be 1. (True or False)
(e) Place a circle or X to indicate which of the 3 tables below can be discrete probability distributions.
|
X
|
P(X)
|
|
10
|
.8
|
|
20
|
-.5
|
|
30
|
0.4
|
|
40
|
0.3
|
|
X
|
P(X)
|
|
-1
-2
-3
|
0.44
0.50
0.06
|
(f) For the following probability distribution determine the mean, variance, and standard deviation (µ, σ2, σ). You may use the extra columns to organize your calculations.
|
X
|
P(X)
|
X · P (X)
|
X2 · P (X)
|
|
5
6
7
|
0.15
0.35
0.50
|
|
|