Question

The probability distribution for the number of students being absent in a class on a Saturday is as follows:

X	0	2	4	5
P(X)	p	2p	3p	p

Where X is the number of students absent.

1.  Calculate p.    [1]
2. Calculate the mean of the number of absent students on Saturday.    [2]

Answer 1

X	0	2	4	5
P(X)	p	2p	3p	p

(i) `sum p_i = 1`

p + 2p + 3p + p = 1 

7p = 1

p = `1/7`

(ii) Mean = `∑ x_i p_i`

 = 0 × p + 2 × 2p + 4 × 3p + 5 × p

= 4p + 12p + 5p

= 21p

= `21 xx 1/7`

= 3