Problem 5: Suppose a discrete random variable X assumes the value 3/2 with probability 0.5 and assumes the value 1/2 with probability 0.5. a). Calculate the expected value and variance of X. b). Suppose that Xı, X2, and X3 are three independent random variables with the same distribution as X. What is the expected value of the sum X, + X2 +X3? The product X,X2X3? Problem 6: Suppose that you have one hundred independent instances of X as defined in Problem 5. Use Markov's inequality to prove that the probability that the product of all one hundred instances exceeds 50 is less than 1/50.
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!
I need help with problem 6.
For 5
A)
B) X1+X2+X3= 3 and X1*X2*X3= 1
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
