Homework Answers

Let X, Y be independent and identically distributed random variables, each having Poisson distribution with rate parameter λ. Find the probability generating function of W = X + Y and hence the mean and variance of W

1) The jdf of the random variables X, Y is given as

f(x, y) = { 2 /5 (2x + 3y), 0 < x < 1, 0 < y < 1

0, elsewhere

find Pr [ 1 /3 < X < 2 /3 |y > 3 /4 ]

A population consists of the four measurements as follow:

5 9 10 8

What is the mean and standard deviation of the population?

Let 𝑆 be any non-empty set and let 𝑉 (𝑆) be the set of all real valued functions on ℝ. Define addition on 𝑉 (𝑠) by (𝑓 + 𝑔)(𝑥) = 𝑓 (𝑥) + 𝑔(𝑥) and scalar multiplication by (𝛼 ⋅ 𝑓 )(𝑥) = 𝛼𝑓 (𝑥). Check that (𝑉 (𝑆), +, ⋅) is a vector space.

Consider the function g defined by:

g(x,y) = cos (xπ "\u221ay" ) + 1/log₃(x - y)

Determine ∂²g/∂y∂x

In a recent survey of 1159 students, 968 of them would like to recommend a website to their friends. Construct a 95% confidence interval to estimate the proportion of all students who would recommend the website to their friends.

Give your answers to three decimals:

_____,_____

A survey of 98 randomly selected students finds that they spend a mean of $435 per semester. Assume that the population standard deviation is $56 per month.

Confidence Interval: What is the 95% confidence interval to estimate the population mean? (Round your answers to two decimal places.)

______ < u < _______

For a normal distribution, assume the 'sample' standard deviation is 8. What is the maximal margin of error associated with a 99% confidence interval for the true population mean if n = 25. ?

(Round to two decimal places)

What is the t value with a 90% confidence interval for the true population mean if the sample size n = 27?

(Please keep three decimal places)

t value= ____________