real analysis – I seem to have a simple problem with job statistics …

I've been struggling with this problem for a while. I'll get right to it. Suppose that $ X $ will be delivered $ N (0,1) $. $ Y $ is distributed normally with positive mean and given variance, and $ Z $ is normally distributed with a positive mean and given variance. All three are independent. I am interested in the following calculation:

$ P (X> min (Y, Z)) $,

What I want to show is that if I increase the variance of either $ Y $ or the $ Z $ variable, this probability increases.

Graphically it seems to work: Imagine your three normal distributions on the same axis. We are interested in when the values โ€‹โ€‹of the variables with the fixed distribution are furthest to the right $ N (0,1) $ is bigger than one of the two on the right. By increasing the variances from either of the two to the right, this distribution becomes flatter and "smoother," and hence the likelihood that $ X $ is larger than this variable seems to be increasing.

The following reference (https://www.untruth.org/~josh/math/normal-min.pdf) is a good way to get an overview of these probabilities. However, it is difficult to prove that their variance increases.

Any help would be appreciated.

Probability – Probability and Statistics

You play a board game in which you throw a four-sided dice and an unfair coin, which yields a head with a probability of 1/3 and a number with a probability of 2/3. How to calculate the score:

โ€ข If you get a head by coin toss, your score is twice as high as the one you received from the throw.

โ€ข If you get a toss from the coin toss, your score is the number you received from the toss, plus 1.

(a) Write down the rehearsal room of this game. (Note: Write down all possible combinations of die and coin outcome.)

(b) Let the random variable X be your score. Find the probability mass function of X.

(c) Find the cumulative distribution function of X.

statistics – What is $ t $ in $ E?[e^{itX}]$?

I consider the characteristic function of a random variable. I do not understand why it's less than or equal to 1 because I see Mean Function on random variable ($ E (e ^ {iX}) $), which could be larger than 1. And t, which I do not understand at all, is my 1st suspect.
Could someone explain the role to me $ t $?

Referring to my last comment after researching my own question, on How are the complex functions built? (here: How to get from Fourier transformation with imaginary numbers those with real numbers?)

Statistics – There are 10 men and 10 women. How many options are there to arrange these 20 people at a round table with 25 seats?

There are 10 men and 10 women. How many options are there to arrange these 20 people at a round table with 25 seats? (Twists are considered the same arrangement.)

Is it just a simple permutation problem of 25P10 = 25! / 15! or does the fact that it's a circle change things?

Statistics – probability with two boxes and two differently colored balls to draw a color after two balls have been moved.

(There is already a similar question to this question, but it has no accepted answer …, so ๐Ÿ™‚

There are two boxes indicated. There are 15 white and 12 black balls in the first box and 14 white and 18 black balls in the second box. Anna delivers the following experiment. Anna places her hand in the first box, immediately takes two balls and places them in the second box. Then she takes a ball without looking out of the second box.

What is the probability that she took a white ball from the second box?

My approach is to first calculate the probabilities of the 4 possible cases to move two balls: {(WW), (WB), (BW), (BB)}.

And then multiply the resulting probabilities by the new second box amounts. Finally, I would add the four resulting values.

For example. For (WW) I would do:

  1. Draw WW: $ frac {15} {27} * frac {14} {26} about $ 0.3
  2. Calculate the probability of drawing white from the second field: $ 0.3 * {frac {16} {34} about $ 0.14

But I'm not even sure if I have to differentiate between (B, W) and (W, B)

dnd 5e – Design a statistics block for a 5e-hieracosphinx

The Hieracosphinx is a smaller sphinx that has no official statistics block for 5e, as in Christopher Perkins. Twitter, However, I would like to use this monster in a desert environment with Level 6 characters, for whom the stronger Gynosphinx (CR 11) and Androsphinx (CR 17) are out of the question, to be too strong and not evil. In 3e, which I'm not at all familiar with, the hieracosphinx seems to have a CR of 5, see here, but I have no idea if I could translate the values โ€‹โ€‹1 to 1 in 5.

Another idea I had was to increase a Griffon (CR 2) and give him the Gynosphinx Claw Multiattack, a bit more HP, and a few magic spells from the Spell List.

So how do I make a hieracosphinx for this issue? I've never designed a monster from scratch, just sometimes added 1 or 2 things to existing monsters or subtracted them from them.

Statistics – Looking for which formula with what probability?

In East Baton Rouge, Louisiana, 88% of all households have an LED TV, and 25% of all households have Wii. The likelihood that a household will have an LED TV when it has Wii is 58%. What is the likelihood that a household will have both LED TVs and Wii?

I'm a little confused about the way this question is written because I understand that 88% LED TV, 25% Wii, then the probability of having an LED and a Wii is 58%. Is the question about TV and Wii or about a LED with Wii? If so, which formula is best used? I would think it would be = p (a) + p (b) – p (a | b), but I'm not sure that's right.

Every help is appreciated !!

Statistics – A / B Testing – How do I deal with minorities who have chosen B?

& # 39; C # 39 ;.

Option C should be a working model that introduces the compromised hybrid solution, which seeks to calm both test groups to a higher percentage. It will always change and refine its processes through many micro-updates that are gradually changing the UX. Of course this requires a lot of resources, your undivided attention and much more – so often the answer is "nothing". They do nothing against the people who have the option & # 39; B & # 39; to prefer. They found a way to steer the scale in the right direction, and have dealt with Layout & # 39; A & # 39; resigned.

Statistics – Need help with the probability question

Respondents are concerned about the decline in cooperation between people contacted in surveys. One pollster contacts 85 people aged 18 to 21 and finds that 72 of them answer and 13 refuse to answer. If 293 people between the ages of 22 and 29 are contacted, 275 and 18 will refuse to respond. Suppose 1 of the 378 people is randomly selected. Find the chance of finding someone between the ages of 22 and 29 or someone who refuses to answer.