1. A professor gives bonus points for attendance using the following algorithm. A random number between 1-100000 is generated first. If the number is odd then a second number is generated within the same range and the bonus points equal the remainder of the division of the second number by 5. If the first number is even there will be no bonus points. a. Find the density of X= bonus points for a single class day. b. What is the probability that in one day the bonus will exceed 3 points? 2. If Y=X1+X2 where X; i=1,2, are the bonus points of class days 1 and 2 (use the previous problem statement to define the bonus) respectively find the density function of Y. Give the probability that the total bonus for days 1 and 2 is no more than 1 point.
1. A professor gives bonus points for attendance using the following algorithm. A random number between 1-100000 is generated first. If the number is odd then a second number is generated within the same range and the bonus points equal the remainder of the division of the second number by 5. If the first number is even there will be no bonus points. a. Find the density of X= bonus points for a single class day. b. What is the probability that in one day the bonus will exceed 3 points? 2. If Y=X1+X2 where X; i=1,2, are the bonus points of class days 1 and 2 (use the previous problem statement to define the bonus) respectively find the density function of Y. Give the probability that the total bonus for days 1 and 2 is no more than 1 point.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Transcribed Image Text:1. A professor gives bonus points for attendance using the following algorithm. A random number between 1-100000 is generated first. If the
number is odd then a second number is generated within the same range and the bonus points equal the remainder of the division of the second
number by 5. If the first number is even there will be no bonus points.
a. Find the density of X= bonus points for a single class day.
b. What is the probability that in one day the bonus will exceed 3 points?
2. If Y=X1+X2 where X; i=1,2, are the bonus points of class days 1 and 2 (use the previous problem statement to define the bonus) respectively
find the density function of Y. Give the probability that the total bonus for days 1 and 2 is no more than 1 point.
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