Please help. Variance of X. V(X)?
In a shooting workout, a basketball player will keep shooting until he makes 10. If the probability that he makes a shots 0.7, and X let be the total number of shots he will take, calculate. V(X)=?
- nbsaleLv 62 years agoFavorite Answer
Let X = random variable = the number of shots it takes for him to make 10.
First look at the probability that he makes 9 of 9+k shots, which is
q(k) = (0.7^9)(0.3^k) C(9+k,9)
Then P(X=10+k) = .7q(k).
We have to do it this way, because X = 10-k means that he makes exactly 9 out of 9+k, then makes the next shot.
Now add that up for k = 0 to some reasonably large number, and you get that
E(X) = 14.28517 = 100/7
V(X) = 6.12244898
Screen print part of my Excel spreadsheet is shown below, based on about 50 shots.
I don't have an exact expression for V, but it might be 6 6/49, which is correct to 10 decimal places. This is pushing Excel's limits, but i think it's a good bet that 6 6/49 is the exact answer.
- PopeLv 72 years ago
You may have gotten a bit trigger-happy with the Best Answer button. The answer you chose is correct though.
You have defined a negative binomial distribution with the following parameters:
p = 0.7
r = 10
V(X) = r(p - 1)/p²
= 10(1 - 0.7)/0.7²