Question

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

Answer 1

Answer:

c) 0.1

P(5) = 0.1

Step-by-step 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