#### Probability of an oblique impact

The solar system as it exists today has been shaped by large impacts that happened during the formation of the planets. Some of those impacts have been argued to have been oblique impacts. An example is the impact that formed the Imbrium basin on the Moon: https://news.brown.edu/articles/2016/07/...

#### Expectation value of the maximum of two variables

Consider n variables drawn independently from an arbitrary probability distribution. We derive the general expression of the probability density for the kth largest variable. Derive the general expression for the expectation value of the largest variable. Evaluate this expectation value for the sta...

#### Calculus and Probability

Please see the attachment for the full questions. The graph of a function f: [-2, p] -> R is shown below. The average value of f over the interval [-2, p] is zero. The area of the shaded region is 25/8. If the graph is a straight line, for 0 <= x <= p, then the value of p is: a. 2 b. 5 c....

#### Find the probability using Bayes' Theorem

Assume breast cancer affects .006 of the female population between 45 and 55 years of age. There are two kinds of positive test results: * True Positive (the test indicates you have a disease, and you actually have it.) *False Positive (the test indicate you have a disease, but you actually do no...

#### Linear Programming: Minimziation of cost

Problem 2 - Dog Breeder A large breeder of a particular type of dog wishes to determine the quantities of available types of dog food that he should stock so that he can be assured that his dogs meet their nutritional requirements, but at the least cost possible. He has decided that he can do th...

#### Some questions on normal distribution

(NOTES) calculate the z-value using the appropriate formula z=x−μ σ z=x−μ σ and find the area under the curve for z-value. Normal distribution is calculated by subtracting upper limit area from lower limit area (Round all answers to three decimal places) The mean gas mileage for a h...

#### Statistics: Frequency Distributions

I have two questions. Please use Microsoft word to write out solution. 1) The scores in Mathematics of 15 students are given below. Find range, sample variance and standard deviation. 93 85 78 79 97 90 82 61 53 63 94 69 84 67 95 Show and explain your steps. 2) The following are...

#### math 540

Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the av...

#### Probability, Counting and Combination

See the attachment. 1) When dealing with probability using a dice, let's assume we have a two fair, 6-sided dice that are rolled together. a) What is the probability of the sum of the numbers on the dices to be 8 or larger? b) What is the probability of rolling a 12 on the dices? c) I...

#### Statistics: Replacement and Probability

See the attachment. 6. A coin and a die are tossed. What is the probability of getting a head on the coin and a 4 on the die? Franco has a bag with four letter tiles in it. All of the tiles are the same size and shape, as shown below.(see attachment). One face of each tile has a letter on it, ...

#### Probability: Possible Values

Q1. The function g: [-a,a] --> R, g(x) = sin(2(x-pi/6)) has an inverse function. The maximum possible value is a is:_____. Q2. Harry is a soccer player who practices penalty kicks many times each day. Each time Harry takes a penalty kick, the probability that he scores a goal is 0.7, independent...

#### Expected commission for a salesman

Based on past records, a salesman expects a \$0 commission with probability 0.19, \$1000 with probability 0.2, \$2000 with probability 0.41 and \$3000 or \$4000 both with probability 0.1. Find the expected commission for the salesman.

#### Expected Value and Law of Large Numbers in Roulette

American roulette has 38 equally sized spaces two spaces are green and have numbers 0 and 00 on them and the rest numbered from 1 to 36. Half of the non-green spaces are red and half are black. The three-number bet, also a "row bet", is a bet on the three numbers in a vertical row on the roulett...

#### Maximum Likelihood Estimate & Fisher Information

A random sample of n observations is taken from a Poisson distribution with menu theta and the probability mass function attached. a) Write down the likelihood function b) Use the method of maximum likelihood to find the maximum likelihood estimator for theta. Confirm that you have located a maxi...

#### Probability Calculations: Bob's Umbrella

According to Bob, the payoffs of the several outcomes are as follows: a. If it is sunny and he is not carrying and umbrella, 10 b. If it is sunny and he is carrying an umbrella, 8 c. If it is rainy and he is not carrying an umbrella, 2 d. If it is rainy and he is carrying an umbrella, ...