Stats ques.

"I have a die with six faces numbered consecutively from 1 to 6. What is odd about it is that the probability of rolling the face with the number k is c*q^k, where c is a constant and q=0.96 What is the expected value of the roll of the dice"

I'm abit puzzled why I'm getting a wrong answer. The answer is 3.3811 according to mark scheme.
Don't you just integrate k*c*q^k between 1 to 6. As for c I got 0.191798..

"I have a die with six faces numbered consecutively from 1 to 6. What is odd about it is that the probability of rolling the face with the number k is c*q^k, where c is a constant and q=0.96 What is the expected value of the roll of the dice"

I'm abit puzzled why I'm getting a wrong answer. The answer is 3.3811 according to mark scheme.
Don't you just integrate k*c*q^k between 1 to 6. As for c I got 0.191798..

Yikes.. integrating kcq^k wrt k sounds like a nasty business, how did you do it?

I've not completed this question myself, but the distribution is discrete, not continuous, so your integration should be a summation.



For interest's sake, in this case you would write $q^k=e^{k\ln(q)}$ and proceed from there.

Yikes.. integrating kcq^k wrt k sounds like a nasty business, how did you do it?

I've not completed this question myself, but the distribution is discrete, not continuous, so your integration should be a summation.

Ah, I see. Not something you come across at A-level though I was thinking of using the definition of integration in the discrete case too, and it should get them the right answer. .