Question

Suppose the possible values of a random variable are -3, 5, 10 and that P(10)=0.2. If the mean of the random variable is 4, what are P(-3) and P(5)?

Answer 1

From the given data, the following Table is calculated:

x	p	xp
- 3	a	- 3a
5	b	5b
10	0.2	2
Total =	a +b + 0.2	- 3a + 5b + 2

Since Total Probability = 1, we get:

a + b + 0.2 = 1

i.e.,

a + b = 0.8                   (1)

Given:

Mean = 4

So,

we get:

- 3a + 5b + 2 = 4

So,

- 3a + 5b = 2                      (2)

3 X (1):

3a + 3b = 2.4                      (3)

(2) + (3):

8b = 4.4

So,

b = 0.55

Substituting in (1) we get:

a = 0.55 = 0.8

So,

a = 0.25.

Thus, the answers are:

P(-3) = :0.25

P(5) = 0.55