(a). The random variable X is the number of siblings of a student selected at random from Professor Appiah's Introductory Statistics class. It's probability distribution is given in the following table.
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
|
P(X=x)
|
1/4
|
1/3
|
1/6
|
7/48
|
1/16
|
1/24
|
Find the following
(i). The expected value of the random variable X.
(ii).The standard deviation of the random variable X.
(iii).The variance of the random variable X.
(b).Let Y represents the number of Boys in families having three children. List all possible birth order permutations for families having three children and give the value of Y for each outcome and their associated probabilities [Hint: a family of three is made up of Boys and Girls]. Use your probability distribution to find the following
(i). The mean of the random variable Y.
(ii).The standard deviation of the random variable Y.
(iii).The variance of the random variable Y.