Question

Haval volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.

1.Define the random variable X, and what values does x take on?

2.Construct a PDF table.

3.Find the expected value

4.Find the standard deviation

Answer 1

Ans:

1. X is a random variable that denotes the number events haval volunteers in a month. x take values 0,1,2,3,4,5

2.PDF table :   

x	P(x)
0	0.05
1	0.05
2	0.10
3	0.20
4	0.25
5	0.35

3. Expected value :

= {0P(0)}+{1P(1)}+{2P(2)}+{3P(3)}+{4P(4)}+{5P(5)}

= 3.6

4. Variance =

Now

=15

Since variance of x var(x)= 15- (3.6)² = 2.04

Therefore standard deviation =

=

= 1.429