1. ## [SOLVED] Binomial Geometric

A= X B(3,1/6)
B= X Geo (1/2)

Find

i) P(B>2)
ii) P(A=B)

thanks

2. Originally Posted by gracey
A= X B(3,1/6)
B= X Geo (1/2)

Find

i) P(B>2)
ii) P(A=B)

thanks
Do you mean that A is a random variable that has a binomial distribution with n = 3 and p = 1/6?

Do oyu mean that B is a random variable that has a geometric distribution with p = 1/2?

If so, then:

i) Two options:

1. $\Pr(B > 2) = 1 - \Pr(B = 1) - \Pr(B = 2) = 1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$.

2. From the cdf, $\Pr(B > 2) = 1 - \Pr(B \leq 2) = 1 - \left[1 - \left(1 - \frac{1}{2}\right)^2\right] = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$.

ii) Pr(A = B) = Pr(A = 1 | B = 1) Pr(B = 1) + Pr(A = 2 | B = 2) Pr(B = 2) + Pr(A = 3 | B = 3) Pr(B = 3)

Assuming A and B are independent:

= Pr(A = 1) Pr(B = 1) + Pr(A = 2) Pr(B = 2) + Pr(A = 3) Pr(B = 3)

$= \left[ 3 \left(\frac{1}{6}\right) \left(\frac{5}{6}\right)^2 \right] \left(\frac{1}{2}\right) + \left[ 3 \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right) \right] \left(\frac{1}{2}\right)^2 + \left[\left(\frac{1}{6}\right)^3 \right] \left(\frac{1}{2}\right)^3 = .....$

3. thankyou that is excellent