Suppose that a quality control engineer wishes to test the durability of a child’s toy, the Widgetron. In order to do so, she repeatedly drops the Widgetrons from a height of one metre until the toy breaks on impact. The number of drops until breakage, call it y, is recorded. We will assume that the probability that the toy will not break stays constant from drop to drop, and this probability is independent of the number of times it has been dropped. If we define the random variable, Y, to represent the number of drops until the toy breaks, an appropriate probability model for the random variable Y would be a Geometric model with parameter θ.How is θ interpreted in the context of this model?

Question

Suppose that a quality control engineer wishes to test the durability of a child’s toy, the Widgetron. In order to do so, she repeatedly drops the Widgetrons from a height of one metre until the toy breaks on impact. The number of drops until breakage, call it y, is recorded. We will assume that the probability that the toy will not break stays constant from drop to drop, and this probability is independent of the number of times it has been dropped. If we define the random variable, Y, to represent the number of drops until the toy breaks, an appropriate probability model for the random variable Y would be a Geometric model with parameter   θ.How is   θ interpreted in the context of this model?

canhaulatlt · Accepted Answer

Step 1Y the count for drops until breakage, is the random variable. It is not a parameter.If   θ is the parameter for this (one-shifted) Geometric Distribution, we would write   Y  ∼            G      e      o        1    (  θ  ).Step 2      P    (  Y  =  k  )     =     (  1  −  θ      )          k      −      1        θ               1              k      ∈      {      1      ,      2      ,      …      }      What does this parameter represent in this particular situation?

Answered question

Answer & Explanation

New Questions in High school geometry