Question

A bag contains five tokens numbered 2, 3, 6, 7, and 8. Two tokens are taken in succession out of the bag without replacement. A) Create the probability distribution for "x" being the number of odd numbered tokens drawn. B) What is mean and variance of the probability distribution?

Answer 1

Answer and Step-by-step explanation:

A) Probability of taken two odd numbered token without replacement:

P(3) = 2/5 = 0.4

P(7) = 1/4 = 0.25

Construct a probability distribution:

X 3 7

p(X) 0.4 0.25

B) Mean of the probability distribution:

E(X) = ∑xp

E(X) = 3*0.4 + 7*0.25

E(X) = 2.95

Variance of the probability distribution:

V(X) =
`\Sigma X^(2)p - [E(X)]^(2)`

V(X) =
`3^(2)*0.4+7^(2)*0.25 - (2.95)^(2)`

V(X) = 7.1475

Mean and variance of the probability distribution are 2.95 and 7.145, respectively.