 ### The joint density of x and y is f(x y)=c(x^2-y^2)e^{-x}. Find the conditional distribution of Y, given X=x.

[ f(x, y) = c (x^2 – y^2) hspace{0.5in} 0 leq x lt infty, hspace{0.2in} -x leq y leq x ] This question aims to find the conditional distribution of the given function with a given condition X=x. Read moreLet x represent the difference between the number of heads and the number of tails obtained when […]

### Several factors are involved in the creation of a confidence interval. In regards to the concept of confidence level, margin of error and sample mean, which of the following statements are true?

Reducing the margin of error while keeping the sample size constant will decrease the confidence. The margin of error will be smaller for a bigger sample size if the confidence level is constant. The confidence will increase for a larger sample size if the margin of error is fixed. If the sample size is doubled […]

### Prove that if m and n are integers and m x n is even, then m is even or n is even.

This problem aims to familiarize us with the method of poof. The concept required to solve this problem is related to discrete mathematics, including direct proof or proof by contradiction, and proof by contrapositive. There are multiple methods to write a proof, but here we are going to see only two methods, proof by contradiction […]

### What is stated by the null hypothesis for the chi-square test for independence?

This problem aims to familiarize us with the concept of the null hypothesis and the chi-square test for independence. This problem uses the basic concept of inferential statistics in which null-hypothesis helps us test different relationships among different phenomena whereas the chi-square test determines the relationship among the variables encountered in that phenomena. In inferential […]

### A seafood festival organizer is interested in performing a statistical analysis as per details given below. Which test should be performed?

The organizer of the seafood festival is hosting a clam chowder competition with the following conditions: – There are twelve restaurants that are participating in this contest. Read moreLet x represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible […]