Working on some calculus drills to improve speed and accuracy. This is the first one… plain ol’ derivatives:

Working on some calculus drills to improve speed and accuracy. This is the first one… plain ol’ derivatives:

$latex\sqrt{x}\$

clearly this is not working… okay, I’m just trying to type a square root of x without going to codecogs for my code block…

how about…

[latex]sqrt{x}[latex]

nope. Okay, do I even *have* Jetpack with MathType installed? IDK.

I’ve got all these great news ideas and problems for/about probability and counting… but need to work out my mathtype so I don’t have to go to a website or create images for my equations. Stand by…

Darth Vader was a survivor, and so this approach, which employs the “survival function” will be referred to as The Darth Vader Approach.

The survival function is what is left over from your probabilities once you have summed up the probabilities up to a given value of your random variable *X = x*. In this way, we can define the survival function as follows:

The Darth Vader Approach utilizes the survival function to find the expected value of a random variable by simply summing from zero to infinity, and it works in the discrete case:

…and in the continuous case:

…and in mixed cases, we simply add the discrete and continuous portions together.

What is the advantage of this approach?

It is a short-cut to the expected value, especially in cases where the cumulative distribution function F(*x*) is known, but the probability density function, *f*(*x*) is not known.

NOTES:

section B 1-2 & 1-3

section B 1-4

section B 1-5

section B 1-6

section A 1-7

PRACTICE:

Math 2 Lesson 1-2

Math 2 Lesson 1-3

Math 2 Lesson 1-4

Math 2 Lesson 1-5

Math 2 Lesson 1-6

Math 2 Lesson 1-7

To prepare for Test 1:

Do the Chapter Review questions 1-35 on pages 58 through 61, and watch each of the videos at the Chapter 1 Virtual Nerd™ Video Tutorial link. Remember, you can use your phone to access those videos by holding your camera over the QR code at the beginning of each section in your text. You should also use the interactive links for each section as you work through the problems in your workbook. You only need to know the definitions, postulates, and theorems that are in Chapter 1.

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