 # Questions Flashcards Preview

## Mathematical Modelling and Analysis > Questions > Flashcards

Flashcards in Questions Deck (46):
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## Do the first part of the question. What is the question trying to convey? 2

## What should you think about doing when your see this type of question? 3

## How would you solve this? ### If the argument is the same magnitude but a different sign then the value must be on the opposite side of the pi circle, offset by pi. 4

## How would this question be solved? ### We know that the conjugate has the opposite sign for the complex number part of the cartesian representation.As such if arg(z) has a positive ratio between b and a, arg(z) for the conjugate must be a negative ratio. 5

## How do you solve this?How would you start solving the dimensions? ### Define all the units that are used. They should form a product with each other, and each dimension should have a power. With respect to the variable whose dimension you're trying to find, define the powers. Solve each of the power equations obtained. For example, if the variables come out as being dimensionless, all the powers should be equated to zero. 6

## What did need to remember about these questions 7

## Besides solving the questions, what is an important thing to remember about differentiating when there are two variables in a term?  8

## How would this be solved?  9

## ?What do you need to remember about question b) ### When diff. Bte-t remember that you need to apply the product rule since you're multiplying two varaibles. 10

## Solve C)  11

## Solve d)  12

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## Solve c)  14

## What is the order and degree of this differential equation? What do you need to remember?  15

## Linear and Non-linear  16

## Why do we need to transform non-linear equations. ### Solutions to linear equations can be expressed in terms of a general solution, which is not usually the case for non-linear equations. Linear solutions have explicitly defined solutions while non-linear equations do not. Also, non-linear equations may or may not have implicitly defined solutions. 17

## In other words, find the expectation.  18

## Obtain an expression for the probability that the manufacturing plant will fail within a time 𝑡0 of continuous operation.  19

## Calculate d) given that the expected value(mean time to failure) was found to be 1/VcWhat did you learn from this question? ### That E(X2) applied to function turns out to be equal to E[x2f(x)].  That you can factor out a variable from a integral, to convert it to an integral you know the value of. Bear in mind if you are factoring out a variable, it can't be the variable you're integrating against. 20

## Solve e) given that the probability the plant is going to fail within time t 0 was calculate to be 1−𝑒vc*t0 .  21

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## When asked to find a confidence interval for a normal distribution and the z-values do not exactly add up, do you take the lower or higher value? Using the normal distribution table what is the answer for 6)? 24

## What do they mean when they say "The proportion of all manufactured items of a certain kind that are defective is 0.04 . Use this to estimate the probabilities that in a batch of 100 of these items" 25

## When you need to calculate the probability that something is going to occur in the future (poisson), what equation do you use? 26  27

## How would you go about solving this type of question? ### In the hints, they indicate that you need to maximize the compound probability. You can do that by minimising the function in the sum.To find minimum find derivative wrt a.From observation, we can see that the sum of xt divided by n is equal to the mean of the product of the two variables multiplied. Similarly for t2 . The current equation does not exactly match,  so divide by 2 and n. Transpose mean of xt and t2 into the equation. 28

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## ?What do you have to remember about this question ### That you cannot split a derivative term such as dt across two terms. If it is split, arrange the expression in such a way that both sides have one term. 30

## How do you find the probability distribution function if isn't given in the formula booklet?

### Using the equations under the cumulative distribution function section. It is important to classify the data you're looking at properly. Is it continuous or discrete? 31

## When calculating the mean/expectation of a function what do you most likely need to do ? Example attached. ### Using integration by parts. 32

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## When you have to integrate a function like the one attached, what should come to mind? ### Using the Gaussian integralsThe one you need to use is attached below. 34

## What is the equation for the 95% confidence interval? 35

## What is the Gaussian integral of this function?  36

## What is the gaussian integral of this function  37

## How do you solve this ?  38

## solve c)  39

## If you get this sort of sinusoidal signal, how should you represent it ?

### Using complex numbers. 40

## Solve!  41

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## How do you calculate the z score ?

### where x is a data point mu the mean and sigma the std deviation 43

## When do you use this equation for confidence interval calculation? 44

## What is the category of this differential equation? 45

## Suppose, the historical record shows that annual rainfall in a certain catch basin follows N(60, 15) (inches)What is the probability that in a future year the annual rainfall exceeds 70 (inches)?

### remember that the phi(2/3) is referring 1/sqr(2pi) * exp(-0.5z2) 46

## If you have got the following normal distributions what would be the combination of the normal variables?Given that they are mutually independent. ### Note how the standard deviations have been squared and have an overarching square root. 