Hi, I am stuck on the last step. What am I supposed to do now?
Problem: Let T(n)=3T(n-1)+2, T(1)=2. Prove by induction that T(n)=3^(n-1)
Here is what I have so far:
Show base case k=1: T(1) = 3^1 - 1 = 2
Show for k=n-1: T(n-1) = (3^((n-1)-1)) -1
Show for k=n :
3((3^(n-2)) - 1) + 2
For the exponential density f(x) = 3e^-3x, compute the actual probability for k=3 and k=4.
Expected value = 1/3. The variance is 1/9 and the standard deviation is 1/3 so for k=3 I got:
(1/3) - 3*(1/3) < X < (1/3) + 3*(1/3) (Wasn't sure about this, all I did was sub 2 with 3 from the problem where k=2.)
= -2/3 < X < 4/3
So to get the probability, you integrate f(x) from -2/3 to 4/3? Would this be correct?
Hi, how do I prove that the sum of all the probabilities is equal to 1 for this problem?
Flip a coin until heads show, assume that the probability of heads on one flip is 4/5. We define a random variable X = the number of flips.
a) What are the possible values of X?
b) Find the probability distribution for X: give the first four values and then find a general formula for the probability that X = n
c) Prove that the sum of all probabilities is 1 using the formula for the sum of a geometric series.
p(1) = 4/5
p(2) = 4/25
p(3) = 4/125
p(n) = ((1/5)^n-1) * (4/5)
Hi, I am a bit confused about this problem.
For each of the following random variables, tell whether it would naturally represent a finite, discrete or continuous random variable. Explain your reasoning.
a) X is the number of customers who walk into a shop between noon and 1PM on some particular day.
b) X is the amount of orange juice in a randomly chosen 8-ounce carton of juice.
c) X is the amount of times you play the lottery until you win? We'll assume that once you win you stop playing.
d) X is the number of women in a randomly chosen sample of 500 New York City residents.
For the answers I got:
a) Finite because the amount of people between the noon and 1PM are countable.
b) Continuous because the amount of juice is uncountable.
c) Continuous because you don't know when you will win.
d) Discrete because it is taking a number of people from a set amount.