Consider the following recurrence, defined for n a power of 4 (for the time of some algorithm): T(n) = 3 if n = 1 2T(n/4) + 4n +
1 otherwise (a) Calculate T(16) by hand. Show your work. (b) Use the tree method to solve the recurrence exactly, assuming n is a power of 4. (c) Use the formula to calculate T(1). Show your work. (d) Use the formula to calculate T(4). Show your work. (e) Use the formula to calculate T(16). Show your work. (f) Use Mathematical Induction to prove that your formula is correct in general.
1 answer:
You might be interested in
Answer:
The correct Answer is 0.0571
Explanation:
53% of U.S. households have a PCs.
So, P(Having personal computer) = p = 0.53
Sample size(n) = 250
np(1-p) = 250 * 0.53 * (1 - 0.53) = 62.275 > 10
So, we can just estimate binomial distribution to normal distribution
Mean of proportion(p) = 0.53
Standard error of proportion(SE) = =
= 0.0316
For x = 120, sample proportion(p) = =
= 0.48
So, likelihood that fewer than 120 have a PC
= P(x < 120)
= P( p^ < 0.48 )
= P(z < ) (z=
)
= P(z < -1.58)
= 0.0571 ( From normal table )