a die is modified so that the probabilities of the six possible results are in p

Question

a die is modified so that the probabilities of the six possible results are in proportion to the possible results; i.e. the probability of rolling a two is twice the probability of rolling a one, the probability of rolling a three is three times the probability of rolling a one, the probability of rolling a four is four times the probability of rolling a one, the probability of rolling a five is five times the probability of rolling a one, and the probability or rolling a six is six times the probability of rolling a one.
a. what is the probability of rolling a 6?
b. what is the expected value of the result of a roll?
c. What is the variance of the result of a roll?

Explanation / Answer

a)

Since the total probability should be 1.

P(X=x) = x/(1+2+3+4+5+6) = x/21

P(x=6) = 6/21 = 2/7 = 0.2857

b)

Probabilities are as follows:

Expected value = Sum(x*P(x)) = 1*(1/21)+(2*2/21)+(3*3/21)+..... = 4.333

c)

Variance = sum((x-mean)^2*P(x)) = 2.222

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.