This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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9 views

Chernoff type bounds for negative binomial distribution

If I recall correctly I remember reading that we cannot get Chernoff type results for the negative binomial distribution because of something regarding lebesque measure. I don't quite know all the ...
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1answer
17 views

integral over domain $1_{(x+y≥100)}$

The problem is: Compute: $\frac {1}{40^2}\int_{40}^{80}\int_{40}^{80} (100-x)1_{(x+y≥100)}dxdy$ my attempt: $$=\frac {1}{40^2}\int_{40}^{80}\int_{100-x}^{80} (100-x) dydx = \frac ...
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0answers
50 views

The probability that a subspace contains a given vector [closed]

For $S$ is a given $k$-dimensional subspace of $R^n$($k\lt n$), and for a random $n$-dimensional vector $\alpha$, the question is how to calculate the probability that $\alpha$ is within subspace ...
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1answer
26 views

Expectancy of a joint density

A machine consists of two components, whose life times have the joint density function $ f(x,y)= \begin{cases} 1/50, & \text{for }x>0,y>0,x+y<10 \\ 0, & \text{otherwise} \end{cases} ...
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0answers
18 views

What does subcopula mean?

In copula concept, what does "subcopula" exactly mean? Does it mean a subset of copula? Would you please explain a little bit in details? Thanks in advance!
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9 views

Decay time distribution with uniformly distributed source

Consider a kind of particle (source) that can decay into some other particle (product) with decay constant $\lambda$, i.e. the p.d.f is $f(t)=\lambda e^{-\lambda t}$, and the source is uniformly ...
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15answers
6k views

If you draw two cards, what is the probability that the second card is a queen?

We had this question arise in class today and I still don't understand the answer given. We were to assume that drawing cards are independent events. We were asked what the probability that the second ...
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0answers
19 views

Suppose the CDF F is a continuous real function and note that this does not imply F is differentiable. [closed]

I am a bit concerned and need a solution to this question especially part (i) & part (ii). Can someone please help me?
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1answer
22 views

How do you count probability from expected value and spread of a discrete variable? [closed]

One garden produces 500kg of fruit on avarage. Another produces 300kg on avarage. (Both yearly.) Their spread is 100kg and 80kg, and their correlation is 0,7. The expected value of both is 800kg. What ...
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1answer
19 views

if the probability a shooter hits the target is equal to .8 then …?

if the probability a shooter hits the target is equal to .8 then the probability that the shooter will correctly hit the target after 10 failed attempt is equal ......? probability of hitting the ...
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0answers
13 views

Probability of error in estimation

We are given the cumulative partition function of the rainy days in march and july. We have a paper, without the name of the month (but we know it is one of these two), on which 14 rainy days are ...
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1answer
50 views

What are the odds?

I am trying to create a unique code for people who create an object in my application. I am wanting to determine the odds of the same unique code being generated. This may depend on how I generate ...
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0answers
79 views

Approximate th Probability of a Sum of 16 Independent Uniform R.V.s

This question has to do with the Central Limit Theorem, uniform random variables, and cumulative distribution functions, I believe, but I'm not quite sure how to apply them all in the proper way. Q: ...
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0answers
18 views

Show that if $P(Y_1 \neq 0) > 0$, then with probability one, $\limsup\limits_{n} X_n = +\infty$, $\hspace{10mm}\liminf\limits_{n} X_n = - \infty$ [closed]

I'm having quite a bit of difficulty with the following problem. Any answer or detailed explanation would be greatly appreciated. Let $Y_1, Y_2, ...$ be bounded iid random variables such that $EY_1 ...
2
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2answers
27 views

Expectation over multiple variable?

So I have come across a question asked by my peers. Define: $$g:=\sqrt{E[|y_r(t)|^2]}$$ Given that $$y_r(t)=\sqrt{t}\cdot h+k,$$ where $h$ and $k$ are independent random variables with variance ...
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1answer
28 views

Probability of tossing a coin 1000 times and coming up with heads

I have this problem on my final review sheet and was wondering if someone can go over it with me You are tossing a fair coin 1000 times. Find what is the probability that it comes up heads (a) $500$ ...
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0answers
13 views

Elementary statistics question (hypothesis test with accuracy of 5% and power of the test) [closed]

We are given a table of the cumulative distribution function (in percentages) of the rainy days in march and july. My question is: How do i construct a test of the hypothesis "The number of rainy dais ...
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2answers
19 views

Probability of losing and gaining money in a card game

I have done some simple flipping coin problems but I am not sure how to solve this one. This is from a review sheet for my final. In each round of a game, three cards are dealt from the standard ...
1
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1answer
23 views

How to calculate the probility of 2 independent events of having same value?

We are learning to calculate the probability of sums and difference of random numbers. Here is the problem: One athlete knows from past experience that the distances of his javelin throws follow a ...
2
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2answers
41 views

Why is an entropy of $\text{log}(n)$ only compatible with the uniform distribution

I have a random variable $X$ and want to show that having an entropy $$ H(X) = - \sum_{i=1}^n p_i \text{log}(p_i) = \text{log}(n)$$ is equivalent to the distribution of $X$ being uniform. Starting ...
4
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2answers
83 views

A fair die is rolled n times. What is the probability that at least 1 of the 6 values never appears?

A fair die is rolled $n$ times. What is the probability that at least 1 of the 6 values never appears? I went about calculating the complement of this, because it seemed to be easier. However, I am ...
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1answer
92 views

Something Isn't Right With My Parking

A few days ago in my Calculus BC class we were given a page of 6 challenging end of the year problems. That was a refreshing change from the drudgery we usually do (WebAssign). One of them went like ...
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2answers
31 views

Uniform distributed variable X:U(-9,9) is given. Find the CDF of Y if Y is..

$$Y= \begin{cases} 4X,\ \ \ |X| \leq 3 \\ 0,\ \ \ \ \ \ |X|>3 \end{cases}$$ My take on it: $$F_Y(y)=0; y\leq-12;F_Y(y)=1; y\geq 12;$$ $$F_Y(y)=\{Y < y \}$$ In class in a similar task we ...
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2answers
24 views

The probability to win in a promotional quiz

In a promotional quiz each player, independently, has the chance of winning 1 000 Euros with probability p. It is obviously bad for the organizer if more than one person wins, but it is also ...
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1answer
25 views

Cauchy iid random variables and Strong Law of Large Numbers (helping understand)

Question: Let $(X_n)$ be a sequence of i.i.d. Cauchy random variables with density $\frac{1}{ π(1+x^2)}$. Use the characteristic function $φ(t) = e^{−|t|}$ of the Cauchy distribution to find the ...
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2answers
30 views

Notation $E[t^X]$ where $X$ is a random variable

I have a quick question which occured in the context of probability-generating functions but maybe the issue is more basic. For a random variable $X$, the probability-generating function is given as ...
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0answers
24 views

What are the chances of 2 choosing the same 10 questions AND same answers? 15 Qs, 5 As [closed]

This is a real world problem. I am not a mathematician, so perhaps I'm already at the wrong site. I teach philosophy and believe that there was cheating on the multiple choice section of an online ...
2
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2answers
19 views

conditional probability question

to get a license, one's need to pass a 3 stages exam. If one's fail in one stage he can not continue to the next stage. The probability he will pass the first stage is $0.9$, if he passed ...
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0answers
15 views

Tail Loss Calculations

Two corporations each have a 4% chance of going bankrupt and the event that one of the two companies will go bankrupt is independent of the event that the other company will go bankrupt. ...
0
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0answers
6 views

Probability from random sample [closed]

A survey reports that 17% of drivers listen to audiobooks in their cars. If you select 70 cars at random, what is the probability that you would find the driver listening to music in less than 10 of ...
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1answer
13 views

Inf is not a stopping time in general

If ${\tau_n}$ , $n=1,2,3...$ are stopping times to a given filtration $F_t$, why in general it's not true to claim that $\inf_n {\tau_n}$ is a stopping time also? Thanks
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1answer
34 views

Validity of conditional CDF proof via PDF integral

Given the question: $$\text{Show that}\ F_X(x\mid A) = \dfrac{\Pr(A\mid X\leq x)}{\Pr(A)}\cdot F_X(x)$$ I have seen the solution via probabilities 'directly'. My question is whether the following ...
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1answer
39 views

Proof conditional probability formula

a question for my homework for probability goes as follows: Given X,Y,U, three discrete random variables, prove the following: $$ p_{X|Y}(i|j) = \sum_{k=0}^{\infty}p_{X|YU}(i|j,k)p_{U|Y}(k|j) $$ The ...
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2answers
19 views

Question Using law of total probability

in a box there 4 coins were $i=\{1,2,3,4\}$. The probability of tail for each coin is: $p_1=0,p_2=0.25,p_3=0.5,p_4=0.75$. a coin is randomly chosen and is thrown over and over until tail ...
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0answers
13 views

Simple Question on Conditional Probability with Two Events [closed]

I have two events $A,B$ and I know that $P(B)=0.7$, I also have : $P(A|B)=0.8$ and $P((1-A)|(1-B))=0.6$ Is it possible for me to work out $P(A)$?
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0answers
21 views

Risk-neutral (i.e. martingale) measure if density is given for a single random variable (i.e. asset)

Let $(\Omega,\mathcal F, P)$ be a probability space. And let $S : \Omega \to \mathbb R$ be a random variable, called an asset, also we are given $\pi > 0$ called a price and some $r \ge 0$ called ...
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1answer
54 views

A question related to reflection principle

Question: $$P(X_1\gt 0, ..., X_n\gt 0, X_n=a-b)=?$$ Its Answer: $= (1,1) \rightarrow (n,a-b) $ that meet neither touch nor cross paths. $=[(1,1) \rightarrow (n,a-b) \ \ \text{all ...
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0answers
23 views

distribution function lebesgue measure

I have a random variable X with law $\mu={2 \over 5} \delta_{2}+{1 \over 5} \delta_{-2}+{1 \over 5}\lambda_{[0,2]}$. ( $\lambda$ is lebesgue measure ) I know $F_{X}(t)=P(X\le t)$ but how can i find ...
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2answers
25 views

Probability distribution of number of columns that has two even numbers in a chart

We distribute numbers $\{1,2,...,10\}$ in random to the following chart: Let $X$ be the number of columns that has two even numbers. What is the distribution of $X$? My attempt: ...
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0answers
16 views

Order Statistics Conditional Distribution

We have a system with $M (M\ge 2)$ random variables. The M variables are related as follows. For each i, 1 to M, $X_i = I_i+Z$, where $I_i$, Z are independent uniform random variables. What is the ...
0
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1answer
50 views

Random Variable $X= U:(0,4)$ is given. Find the CDF of $\min \{ |X-1|, 5-X\}+1$

Random Variable $X= U:(0,4)$ is given. Find the CDF of $Y=\min \{ |X-1|, 5-X\}+1$ X has uniform distribution. So we know that $$Y\in (1,6)$$, therefore $$y\leq 1 \ \ \ F_y(y)=0 ; y\geq6\ \ \ ...
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0answers
26 views

Geometric random variable with conditioning [closed]

John will take probability course again and again until he passes it. However he is only allowed to take the course $n$ times. Suppose each time John's probability of passing is $p$ irrespective to ...
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0answers
20 views

Better chances on a gambling game [closed]

I'm working on a program that I hope it will help me to get better chances on a gambling game. I have a very large database of numbers how occur in this game and my program pass through those numbers ...
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2answers
42 views

for a random variable $X$ with density function $f$, show that $E[g(X)]=\int_{-\infty}^{\infty} g(x) f(x) dx$ [closed]

For a random variable $X$ with density function $f$, show that $$E[g(X)]=\int_{-\infty}^{\infty} g(x) f(x) dx$$ I need some help with it by using the random variable $Y=g(x)$.
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1answer
29 views

Prove that $E[Y]=\int_0^\infty P(Y>y)dy-\int_0^\infty P(Y<-y)dy$

Prove that $E[Y]=\int_0^\infty P(Y>y)dy-\int_0^\infty P(Y<-y)dy$. Should I first prove that $$\int_0^\infty P(Y<-y)dy=-\int_{-\infty}^0 xf_Y(x) dx$$ and $$\int_0^\infty ...
1
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0answers
8 views

Sampling With Replacement No-Repeats

I am about to do a survey on a population of 250 individuals. I will be performing a Two Sample T Test For A Difference Between Two Populations but am having trouble meeting the conditions for the 10% ...
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0answers
19 views

How to distribute two independent rows of bits

Consider two independent rows of 100 bits. The bits are mutually independent and have an equal chance to be 0 or 1. The first row is being read and during that process there is a chance $\epsilon$ ...
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2answers
84 views

Why does normal distribution have the same shape regardless of its parameters?

The formula for normal distribution is quite complicated, it has $\sigma$ in the exponent and in denominator. And no matter what $\sigma$ is, the shape of its pdf is the same (i.e. for example 3 ...
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1answer
25 views

probability of distinct phone numbers

the first three digits of a university telephone exchange area 452. if all the sequences of the remaining four digits are equally likely, what is the probabikity that a randomly selected university ...
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0answers
15 views

Question about inverse of CDF being a real analytic function

Let F: [0,a] -> [0,1] be a continuous, strictly increasing CDF. Assume also F admists a continuous, positive pdf f. Now define the inverse function h(x) as F(h(x))=x. Is h real analytic? If not, what ...