A biased coin with probability of getting head is twice that of tail, is tossed 4 times If a random variable X is number of heads obtained, then expected value of X is :

Options

A. ` ( 2 ) /(3 ) `
B. ` (8 ) /(3) `
C. `2`
D. ` (16 ) /(3) `

Answer

B

Explanation

Let X is number of heads obtained
` p = (2)/(3)` probability of getting head
`q = (1)/(3)` probability of getting tail.


`E(x) = Sum xi pi`
` = 0 (1)/(3^(4)) + 1 xx (8)/(3^(4)) + 2 x(24)/(3^(4)) + 4 xx (16)/(3^(4)) = (216)/(81) =(8)/(3)` ` E (x) = (8)/(3)` .