0

the price of a stock increases with the probability $1/3$, and decreases with probability $3/2$ daily. Let U be the number of days it goes up, after 5 days. What is $var(U)$?

I think the expected value of U is 5 times 1/3 equals to 5/3, but I am not sure if using e.g. $(1 - 5/3) ^ 2 * 1/3 + （2 - 5/3）^ 2 * 1/9 + ...$ is a correct way of finding the variance.

Hanayozz
  • 3

1 Answers1

0

The probability is going up is the same everyday.

Hence the variance is just $5\left( \frac13\right) \left( \frac23\right)$ according to binomial distribution.

Siong Thye Goh
  • 149,520
  • 20
  • 88
  • 149
  • I see, I looked up the wiki page of binomial distribution and did find that the variance is np(1-p). Thank you! will look into closely why the equation is in such form. – Hanayozz Mar 20 '21 at 04:09