Exercise 1 page 197

For which of the following random variables would it be appropriate to assign a uniform distribution? (a) Let X represent the roll of one die.

  1. Let X represent the number of heads obtained in three tosses of a coin.

  2. A roulette wheel has 38 possible outcomes: 0, 00, and 1 through 36. Let X represent the outcome when a roulette wheel is spun.

  3. Let X represent the birthday of a randomly chosen person.

  4. Let X represent the number

Solution

  1. Let X represent the roll of one die.

This is a uniform distribution because each try repesent 1/6

  1. Let X represent the number of heads obtained in three tosses of a coin.

This is not a uniform disribution because you cannot get three heads on every outcomes when you toss 3 times

  1. A roulette wheel has 38 possible outcomes: 0, 00, and 1 through 36. Let X represent the outcome when a roulette wheel is spun. Each outcome has possibilty of occuring when the roulette wheel is spun. Therefore, this is appropriate for uniform distribution
  1. Let X represent the birthday of a randomly chosen person. Birthday can occur in different dates within different dates in 365 days. Therefore it is not appropriate for uniform distribution
  1. Let X represent the number If A represent an infite number of eually likely outcome so we can use uniform distribution