Question

100 point to the first correct answer

Given the discrete random variable X: What is the probability distribution of X if X ~B(2, 5/17)?

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Answer 1

X ~ B(n, p)

Given: X ~ B(2, 5/17)

⇒ n = 2

⇒ p = 5/17

Binomial distribution formula:

`\sf P(X = x) = nC_x (1-p)^((n-x))p^x`

As n = 2, calculate P(X = 0), P(X = 1) and P(X = 2):

`\sf P(X = 0) = 2C0 ((12)/(17))^((2-0))((5)/(17))^0=(144)/(289)}`

`\sf P(X = 1) = 2C1 ((12)/(17))^((2-1))((5)/(17))^1=(120)/(289)}`

`\sf P(X = 2) = 2C2 ((12)/(17))^((2-2))((5)/(17))^2=(25)/(289)}`

**Probability Distribution Table attached**