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)?

Question

asked Sep 1, 2023 183k views

1 Answer

Penguru · Answer 1 · 2023-09-06T18:03:46+0000

Answer:

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**