Question

Consider the following probability distribution:

x	P(x)
1	0.1
2	?
3	0.2
4	0.3

What must be the value of P(2) if the distribution is valid?

A.

0.6

B.

0.5

C.

0.4

D.

0.2

What is the mean of the probability distribution?

A.

2.5

B.

2.7

C.

2.0

D.

2.9

Answer 1

Answer

(1) we know that the sum of all individual probabilities in a probability distribution is equal to 1.

So, we can write it as

P(1)+P(2)+P(3)+P(4) = 1

setting the given values, we get

0.1+P(2) + 0.2+0.3 = 1

or we can write it as

0.6+P(2) = 1

subtracting 0.6 on each side, we get

P(2) + 0.6-0.6 = 1 - 0.6

this gives us

P(2) = 0.4

option C is correct answer

(2) We know the formula for the mean of probability distribution is given as

setting the given values, we get

So, the required mean of probability distribution is 2.7

option B is correct answer