1. No we cannot assume that the network will only provide 4KB/s per customer. It cannot be
assumed that the customers will use the constant 4KB all the time. Sometimes it may be more
or less. Improvements can be made by assuming when customers use the most data and a level
data limit can be set for the customer based upon their requests.
2. It cannot be assumed that schizophrenia and smoking pot are correlated. Another possible
reason for the correlation found could be that those with mental health problems may be more
prone to use drugs.
3. (1.1) a. Sample space experiment 1: upper side of coin shows {Head, Tail}
experiment 2: number on top of die {1,2,3,4,5,6}
experiment 3: ball with number pulled {0,1,2,3,4,5,6,7,8,9}
b. experiment 1 relative frequencies: head: ½ tails: ½
experiment 2: 1 through 6 each have a 1/6 chance of happening
experiment 3: 0 through 9 each have a 1/10 chance of happening
4. (1.5) a. Probability when using coin: P(head)=P(tail)=1/2
Probability that head appears on first throw = ½
Probability that head appears on the second throw in a row is ½*1/2=1/4
Probability that head appears on the third throw in a row is ½*1/2*1/2=1/8
b. Urn has 8 balls marked {1,2,3,4}, four with 1, two with 2, one with 3, one with 4
Probability of choosing ball with 1 is 4/8=1/2
Choosing ball with 2 is 2/8=1/4
Choosing ball with 3 is 1/8 the same is true for 4
c. if out of 52 cards the highest king got selected, reject the card and select another,
reject the king card as many times as it is selected
if a black card is selected the probability is 24/48=1/2
if a card of hearts is selected the probability is 12/48=1/4
if a red card with a prime number {3,5,7} is selected the probability is 6/48=1/8
if a black card with a prime number is selected the probability is 6/48=1/8
5. a. The graph of 2cos(2pi*t) is oscillates from 2 to -2, making the long-term sample mean 0
b. Positive voltage P[2cos(2pi*t)>0]=P[cos(2pi*t>0]=1/2
probability that voltage is ess than -2 P[2cos(2pi*t)<-2]=P[cos(2pi*t)<-1=0
c. If the sampling times are periodic, the results could be altered because if tau=2pi you would
get a reading 1V every time, which would make the long term mean also 1. It still would never
go below -2, but it would read positive 100% of the time