Språkstatistik HT95:06

Class:   06
Date:    950921
Topic:   Exercises 2

Homework exercises 6

1. A bowl contains 7 blue balls and 3 red balls. We take out five of the balls randomly.
   • Determine the frequency function for the stochastic variable E1 describing the number of blue balls taken out of the bowl when the balls are not replaced after taking them from the bowl.
   • Determine the frequency function for the stochastic variable E2 describing the number of blue balls taken out of the bowl when the balls are replaced after taking them from the bowl.
   • Determine the average and the variance for either E1 or E2.

2. We have three coins A, B and C which contain a digit on both sides. Coin A contains digits 3 and 6, coin B 2 and 5 and coin C 1 and 4. We throw all coins and rank them in descending order according to the digit that is visible. If for example the visible digit for A is 3, the one for B is 5 and the one for C is 1, the correct order would be B, A, C. We are interested in the first two of this ranking, here B, A in that order.
   • How many different outcomes for the first two are possible in this experiment?
   • Determine the probability for correctly guessing the first two in the order if one guesses that the most probable pair will occur.
   • Determine the probability for correctly guessing the first two in the order for a random guess.

Note that the second exercise is different from the one presented in class.