Homework 09

Page 363 #11

Xn is a independent random variable. So it's sum is normally distributed. 
Also Xn = Yn+1 - Yn => Yn+1 = Xn + Yn
So Y365 = X1 + X2 + ... + X364 + Y1
From the question Y1 = 100
Also from question E[X] = u = 0
so E[Y1] = 100
Using similar calculation, SD of Y365 = sqrt(365 * 1/4)

1. = 100

pnorm(0, 0, sqrt(365 * 1/4), lower.tail = FALSE)

## [1] 0.5

2. = 110

pnorm(10, 0, sqrt(365 * 1/4), lower.tail = FALSE)

## [1] 0.1475849

2. = 120

pnorm(20, 0, sqrt(365 * 1/4), lower.tail = FALSE)

## [1] 0.01814355

2. Calculate the expected value and variance of the binomial distribution using the moment generating function.

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3. Calculate the expected value and variance of the exponential distribution using the moment generating function.