$p=$
$x=$		P(X = x)  = P(X ≤ x)  = P(X ≥ x)  =

This applet computes probabilities for the geometric distribution $$X \sim Geo(p)$$ where $$X = \mathrm{the\ trial\ on\ which\ the}\ 1^{st}\ \mathrm{success\ occurs}$$

Directions

• Enter the probability of success in the $p$ box.
• Hitting "Tab" or "Enter" on your keyboard will plot the probability mass function (pmf).

To compute a probability, select $P(X=x)$ from the drop-down box, enter a numeric $x$ value, and press "Enter" on your keyboard. The probability $P(X=x)$ will appear in the pink box. Select $P(X \leq x)$ from the drop-down box for a left-tail probability (this is the cdf).

Details

• $f(x)=P(X=x)=(1-p)^{x-1}p$
• $x=1,2,\ldots$
• $0 < p \le 1$
• $\mu=E(X)=\frac{1}{p}$
• $\sigma^2=Var(X)=\frac{1-p}{p^2}$
• $\sigma=SD(X)=\sqrt{\frac{1-p}{p^2}}$