### If X is an exponential random variable parameter, λ = 1 , compute the probability density function of the random variable Y defined by Y = logX.

This problem aims to familiarize us with the probability density functions. The concepts required to solve this problem are continuous random variables and probability distributions, which include exponential distribution and densities of random variables. A probability density function or PDF is used in probability theory to describe the probability of a random variable staying within […]

### Justine works for an organization committed to raising money for Alzheimer’s research. From past experience, the organization knows that about 20% of all potential donors will agree to give something if contacted by phone. They also know that of all people donating, about 5% will give 100 dollars or more. On average, how many potential donors will she have to contact until she gets her first 100 dollars donor?

The main objective of this question is to find the number of calls in order to get a donation of 100 dollars from these calls. This question uses the concept of  Binomial probability. In binomial distribution, we have two possible outcomes for a trial, which is success or failure. Expert Answer We are given that […]

### Determine which plot shows the strongest Linear Correlation.

This question aims to find the linear correlation between different indicator points on the XY-axis. The coefficient of linear correlation indicators analyzes the strength of the linear relationship between different variables. The correlation is called positive if the linear coefficient is greater than zero, and it is called negative if the linear coefficient is greater […]

### The probability density function of x the lifetime of a certain type of electronic device

The probability density function f(x) of a random variable x is given below, where x is the lifetime of a certain type of electronic device (measured in hours): [ f(x) =Bigg{begin{array}{rr} dfrac{10}{x^2} & x>10\ 0 & xleq 10 \ end{array}] – Find the cumulative distribution function $F(x)$ of $x$. – Find the probability that ${x>20}$. […]

### How many ways are there to choose four members of the club to serve on an executive committee?

– There are $25$ members in a club. – In how many ways can $4$ members be chosen to serve in an executive committee? – In how many ways can a president, vice president, secretary, and treasurer of the club be chosen so that each person can only hold a single office at a time? […]