# Math Help - help geo

1. ## help geo

the random variable t can take any values and has a geometric distribution. it is given that p(t=1 or 2)= 0.4375. Find the value of p(t=1)

thanks

2. Originally Posted by gracey
the random variable t can take any values and has a geometric distribution. it is given that p(t=1 or 2)= 0.4375. Find the value of p(t=1)

thanks
Good question:

I am using this function as my pdf: $f(t) = q^{t-1}p \Rightarrow (1-p)^{t-1}p$ where t is the number of trials.

$P(t=1 or t=2) = P(t=1) + P(t=2) \Rightarrow p + qp = p+(1-p)p \Rightarrow 2p-p^2 = .4375$

$p^2-2p+.4375=0$

$p=\frac{2 \pm \sqrt{4-1.75}}{2} \Rightarrow \frac{2 \pm 1.5}{2} = 0.25$

$P(t=1) = p \Rightarrow 0.25$