Question

The following table represents a probability distribution for a random variable, X. What must P(5) be?

Answer 1

c) 0.1

P(5) = 0.1

Explanation:

Given data

x : 0 1 2 3 4 5

p(x): 0.2 0.1 0.3 0.1 0.2 ?

Given data is discrete distribution

if the numbers
`P(x_(i) )` i = 1,2,3..... satisfies the two conditions

i)
`P(x_(i) )\geq 0` for all values of 'i'

ii) ∑P(x) = 1

Given data

i)
`P(x_(i) )\geq 0` for all values of 'i'

ii) ∑P(x) = 1

P(x=1) + P(x=2) +P(x=3) +P(x=4)+P(x=5) =1

⇒ 0.2 + 0.1 + 0.3 +0.1 +0.2 + p(X=5) = 1

⇒ 0.9 +p(5) =1

⇒ p(5) = 1 -0.9

⇒ P(5) = 0.1