S
The sum of the first n natural numbers is $\frac{n(n+1)}{2}$. Prove this.

S
There is no rational number whose square is 2. Prove this.

S
There are infinitely many primes. Prove this.

S
Given a right triangle drawn in the plane, whose legs have lengths a and b, and whose hypotenuse has length c, then $$a^2+b^2=c^2$$ Prove this

H
A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die....

H
Verify that the gamma density function integrates to 1

H
The standard deviation of X, denoted SD(X), is given by $SD(X)=\sqrt{Var(X)}$ Find SD(aX + b) if X has variance $\sigma^2$

H
The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by $$f(n) = \begin{cases} ax^2 e^{-bx^2}, & \text{x... 1 answers and 9 views C Asked by 17 days ago *This scenario applies to Questions 1 and 2*: A study was done to compare the lung capacity of coal miners to the lung capacity of farm workers. The researcher studied 200... 1 answers and 17 views B Asked by 17 days ago I need help solving the equation,$$x^2+4x+4=0

C
**For the following questions, assume that the population standard deviation σ = 5cl.** 1) A machine is set up such that the average content of juice per bottle equals...

C
8) In their advertisements, a new diet program would like to claim that their program results in a mean weight loss ($\mu$) of more than $10$ pounds in two weeks. State the...

C
5). Suppose a consumer advocacy group would like to conduct a survey to ﬁnd the proportion p of consumers who bought the newest generation of an MP3 player were happy with...

C
1. A sample of size $n = 100$ produced the sample mean of $\bar{X} = 16$. Assuming the population standard deviation $\sigma = 3$,compute a $95\%$ conﬁdence interval for the...

C
a) Concept 1. True or false: Setting the prior probability of a hypothesis to 0 means that no amount of data will make the posterior probability of that hypothesis the maximum...

C
1)The following data is from a random sample: $5, 1, 3, 3, 8$. Compute the sample mean, sample standard deviation and sample median.

C
1) Suppose $X$ is a random variable with $E(X) = 5$ and $Var(X) = 2$. What is $E(X2)$?

C
2) More cards! Suppose you want to divide a $52$ card deck into four hands with $13$ cards each. What is the probability that each hand has a king?

C