In a test of weld strength 80 of tests result in a fracture

In a test of weld strength. 80% of tests result in a fracture in the weld, while 20% result in fracture in the beam. Let X denotes the number of failed trials that precede the third beam fracture. What is the distribution of X? Find P(X = 8) Find the mean and variance of X.

Solution

Probability density function The red curve is the standard normal distribution Cumulative distribution function Notation N ( , 2 ) {\\displaystyle {\\mathcal {N}}(\\mu ,\\,\\sigma ^{2})} Parameters R — mean (location) 2 > 0 — variance (squared scale) Support x R