Question

Suppose I work in a factory which does not have the best safety record. On any

given day (independent of all other days) there is a 5% chance that there will be a

workplace injury. Let X be the number of days until we have a workplace injury.

What is the distribution of X? Give the name of the distribution and the

appropriate parameters.

What is the mean and variance of this distribution? Give your answer as a number,

but include the formulas (or logic) used.

What is the probability that there will be an injury within the next 5 workdays?

i.e. what is P(X≤5)

Let’s say a few employees have a rather inappropriate betting pool on which day

the next injury will occur. If I placed my wager on day 4, what is the probability

that I win?

Answer 1

solution a) Xn Geometric distribution þ= 0.05 P(x) = qx 1p - Q=1-6 = 0.gs. Po 0.05 Yaniance - b) Meon dos - | 20 vasionce phone 0.05)2 + 380 () P(x+5) = P1=1) + PH=2) + P1==3) + Plx=4) + P(x=5) 10.959 10.05) wa = 0.926275 0.2262 d) P(x= 4) = (0.95) 10.05) 0.0429 4- 1 00