A jar contains 3 balls: one blue, one red, and one yellow. We repeat drawing balls from the jar with replacement until all three balls are drawn at least once. 1. What is the chance that the blue ball is drawn before the red balls? Answer: 2. What is the chance that the last ball is yellow? Answer: 3. Let N denote the total number of times we draw a ball from the jar in this experiment. What is the expected value of N? (Hint: Write N as a sum 1+ N + N2 where Ni and Nare appropriate geometric random variables.) E[N] =?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A jar contains 3 balls: one blue, one red, and one yellow. We repeat drawing balls from the jar with replacement until all three balls are drawn
at least once.
1. What is the chance that the blue ball is drawn before the red balls?
Answer:
2. What is the chance that the last ball is yellow?
Answer:
3. Let N denote the total number of times we draw a ball from the jar in this experiment. What is the
as a sum 1+ N + N2 where Ni and Nare appropriate geometric random variables.)
E[N] =?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
