Asked by Susanna 14 days ago

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

2 answers and 14 views

Asked by Susanna 14 days ago

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

1 answers and 17 views

Asked by Susanna 14 days ago

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

1 answers and 7 views

Asked by hansel 16 days ago

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....

1 answers and 3 views

Asked by hansel 17 days ago

Verify that the gamma density function integrates to 1

1 answers and 14 views

Asked by hansel 17 days ago

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

1 answers and 4 views

Asked by hansel 17 days ago

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

Asked by chegendungu 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

Asked by chegendungu 17 days ago

**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...

1 answers and 39 views

Asked by chegendungu 17 days ago

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...

1 answers and 19 views

Asked by chegendungu 17 days ago

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...

1 answers and 17 views

Asked by chegendungu 17 days ago

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...

1 answers and 10 views

Asked by chegendungu 17 days ago

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...

1 answers and 9 views

Asked by chegendungu 17 days ago

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

1 answers and 10 views

Asked by chegendungu 17 days ago

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

1 answers and 5 views

Asked by chegendungu 17 days ago

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?

1 answers and 7 views

Asked by chegendungu 17 days ago

1) A full house in poker is a hand where three cards share one rank and two cards share another rank. How many ways are there to get a full-house? What is the probability of...

1 answers and 7 views

Asked by chegendungu 17 days ago

2) A slightly anxious couple has one child (a boy) and is worried that the child may not be eating properly, perhaps causing it to grow more slowly than would be expected. The...

0 answers and 8 views

A certain town with a population of 100,000 has 3 newspapers: I, II, and III

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