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

calculating probability of an event

I have encountered a question The weather report says that there is a P probability of rainfalls today. Raj has to step out for a meeting at the office, and would like to know the probability ...
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0answers
13 views

central limit theorem for function of random variables

Let's say you have $X_1,...,X_n$ observations of a RV X, which is distributed according to some arbitrary prob. function. Further there is a deterministic function $f(X)=Z$, $f: X \rightarrow [-1,1]$ ...
3
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1answer
47 views

How to find a probability?

Two ships, independently arrive, at the port in any time within $24$ hours ($0-24$h). Every moment of arrival of ships is equally possible within $24$ hours. If the port can handle only one ship and ...
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0answers
16 views

Buffon needle problem , scenario $\ell>d$

suppose we have the classic problem of buffon's needle , let $\ell$ be the length of the needle and $d$ the distance between the parallel lines . I have solved the case which $\ell \leq d$ and i ...
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0answers
9 views

renewal process and renewal function

Let $N_t$ a renewal process and $T_i$ the jumps. $T_i=X_1+...+X_i$ and let F the distribution function. Let $(F \star F)(t)=\int_0^t F(t-u)F(du)$ and $U(t)=\sum_{n=0}^{\infty} F^{\star n}(t)$ the ...
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4answers
33 views

pdf is defined as $f_X(x)=P(X=x)$ but isn't $P(X=x)=0$

When we define a probability distribution function, we say: $f_X(x)=P(X=x)$ and thats equal to some function such as a gaussian But isn't $P(X=x)=0$ for a continuous random variable $X$. Is it ...
2
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4answers
66 views

Statistics: Conditional Probability

$P(A│B)=\frac25$ ,$P(B)=\frac14$, $P(A)=\frac13$. Find $P(A\land B)$ $P(B|A)$ Here is what I did: Part 1. $$P(A\land B) = P(A) \cdot P(B)\\ = \frac13\cdot\frac14=\frac{1}{12}$$ Part 2. ...
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0answers
20 views

How could an estimator be biased but consistent according to mathematical definition?

According to the definition, an estimator can be biased, if $E_{\theta}[\hat{\theta}]\ne\theta$, with $\theta$ as parameter for a distribution we want to get from samples. While the estimator can be ...
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3answers
17 views

The probability that the output of the experiment is Y is ___?

Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, ...
2
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1answer
31 views

Conditional expectation $E(XY\mid Z)$

I'm trying to solve the following problem: let $X$ and $Y$ be 2 independent standard normal random variables and let be $Z=X+Y$. Calculate $E(XY\mid Z)$. I tried many approaches, but without getting ...
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1answer
42 views

Expected Value of a in a randomly chosen Rectangle

There is a N×M grid. Each square in the grid either has or does not have a mango tree. For example, suppose the field looks as follows. We Know That there are K Mango Tree. ...
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1answer
18 views

Probabilities for rolling multiple dice and getting one number or greater

I am interesting in producing a table of probabilities for dice rolls. These are standard 6 sided dice. What is the probability that for rolling X dice, Y dice will roll (hit) at least number Z or ...
0
votes
1answer
31 views

Probability of getting a number in a sudoku box when two numbers are already fixed.

Imagine a sudoku box, I named the rows by alphabets like $a,b,c,d...$ And the columns as $1,2,3,4...$ If two numbers were already filled,i,e at $(a,1)$ there is '$1$' and at $(b,2)$ there is '$2$' ...
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3answers
49 views

Does $n/\Sigma_{i=0}^n(1/X_i)$ converge to $0$ in probability for $X_i$ iid standard uniformly random variables?

Suppose $X_i \sim\operatorname{uniform}[0,1]$ and that they are iid. Does $n/\Sigma_{i=0}^n(1/X_i)$ converge to $0$ in probability? A simulation seems to indicate that it does. But as the expected ...
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1answer
9 views

Proof of Probability for Exponential RV's where $ x_1 < x_2$

I have a theorem in my notes that says that if X is an exponential RV, $X$ ~ $exp(\lambda_{1}+\lambda_{2})$, $$Pr(x_{1} < x_{2}) = \frac{\lambda_{1}}{\lambda_{1}+\lambda_{2}}$$ I was too far ...
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1answer
9 views

Determine the transition probability matrix, Simple Insurance Company…

The Simple Insurance Company starts at time $0$ with a surplus of $3$. At the beginning of every year, it collects a premium of $2$. Every year, it pays a random claim amount as shown: $0$ with ...
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0answers
21 views

3 card poker ante bet computation [on hold]

On the 3 card poker, I have came up on the possible combinations that can be generated from a 52 card of deck. and it was correct. now my problem was how they came up with the values of the Ante ...
1
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1answer
28 views

Find the joint probability density given the support set

Suppose that the support set of $(X,Y)$ is $$S_{X,Y}=\{(x,y)\in\mathbb{R}^2: x \geq 0 \text{ and } 0 \leq y \leq e^{-x/3}\}$$ $(X,Y)$ is uniformly distributed on $S_{X,Y}$. a) Find the joint ...
1
vote
1answer
42 views

How many ways are there to arrange these letters? [on hold]

So I've been working out how many ways there are to arrange the letters of probabilistic. I came up with $518918400$ ways. The next thing I want to figure out is out of those ways, how many of them ...
3
votes
1answer
46 views

Almost sure bounded imply finite expectation?

Suppose that the random variable $X$ is $\mid X \mid<M$ almost surely, for some constant $M<\infty.$ Then can we say that $E(X)<C$ for some constant $C<\infty$? If the expectation is not ...
2
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1answer
18 views

Exponential law with both positive and negative values

The exponential law with density $f(x) = \lambda e^{-\lambda x}$ for $x \geq 0$ and $f(x)=0$ for $x < 0$, is well-known. What's the name of the distribution which has $$f(x) = \frac{1}{2} ...
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3answers
35 views

Probability of an odd amount of sixes when rolling a 6-sided die 10 times.

Rolling a fair die 10 times, what is the probability it will give an odd amount of sixes? So the outcomes I'm interested in are: 1 six in 10 rolls or 3 sixes in 10 rolls or 5 sixes in 10 ...
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2answers
35 views

AM-GM Inequality Confusing

Here is something that I find hard to make sense of. Suppose $X_1, X_2, ..., X_n$ are independent draws from some distribution. By AM-GM inequality, we have: $$ \left( X_1 X_2 .. X_n ...
2
votes
2answers
39 views

Proving a Trick to More Quickly Calculate N-Step Transition Probabilities

So, I have been working on a homework problem all day that asks me to prove that: $P^n= \Pi +Q^n$ where P is the transition matrix of a finite-state regular Markov Chain, $\Pi$ is a matrix whose rows ...
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1answer
21 views

probability question: word game

Suppose i have a bag with all letters of the alfabet. I pick $1$ letter and i put it back. I pick like this 20 letters (so duplicates are allowed). I need to calculate the change that i can form a ...
3
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3answers
28 views

Consecutive strings of heads problem

So the question asks: We toss a fair coin $n$ times and record the outcome as a sequence of H and T. We say that there is a run of heads if there is a consecutive string H...H which starts either at ...
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0answers
9 views

Continuous time markov process

If a stochastic time X(t) t $\ge$ 0 is a Markov Process defined on a finite space, then must it be a jump process?
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1answer
15 views

Expected value prove problem

So the question asks: Let Y ≥ 0 be a non-negative random variable. Prove that that for any $t > 0$, P (Y ≥ t) ≤ E [Y ]/t So so ...
0
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0answers
17 views

Expectation of the product of a random variable squared and its third derivative

Here is how the problem is posed. Show: $$ \left \langle u^2\frac{\mathrm{d}^3 u}{\mathrm{d} t^3} \right \rangle = -2\left \langle u\dot{u}\ddot{u} \right \rangle =2\left \langle \left ( \dot{u} ...
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1answer
46 views

How do I calculate dice with addition and subtraction based on dice rolls?

I am trying to figure out how to calculate results on a group of dice where some results are positive and others are negative. Example: I roll a group of dice that are fair and six-sided. Each roll ...
0
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1answer
33 views

Convergence in Distribution to the normal distribution.

let $ X_1,X_2+,...,$ be independent and identically distributed random variables with Poisson Distribution, does $$ \frac{1}{\sqrt{n}}\sum_{i=1}^n(X_{2i-1} - X_{2i})$$ Converge in distribution to ...
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0answers
27 views

another follow up question: modeling with exponential distributions

This a follow up question to the previous two: modeling with exponential distributions a follow up question about modeling with exponential distributions I'm trying to do (c). Denote the ...
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0answers
24 views

Probability to reach final state

Let $~~m,n>0~~$ be some positive integers. We have some system of states. Each state is pair $~~(i,k)~~$ where $~~0\leq i \leq m~~$ and $~~0\leq k \leq n~~$. Starting state is $~~(m,n)~~$. For ...
0
votes
1answer
20 views

CDF of the highest result of multiple unform random variables.

Say I have multiple uniform random variables. I want to know the CDF for selecting the highest result of all the variables. As an example, say I have 3 uniform random variables from [0, 100). Using a ...
0
votes
1answer
17 views

density function of $W = X^2$ when $X$ is uniform with disjoint intervals

I'm having some trouble figuring out this (admittedly) very easy problem. Hoping ya'll could help me figure out where I'm going wrong: Let $X$ be uniform on $(-2,1)$ and $(1,2)$ and derive the ...
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0answers
43 views

Expected Value of a Mangoes [on hold]

There is a $N \times N$ grid. Each square in the grid either has or does not have a mango tree. For example, suppose the field looks as follows: ...
2
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2answers
16 views

Conditional probability - 8 tosses of a coin

We throw a coin 8 times. What is the probability of getting the same number of heads and tails, if on the last three tosses of a coin we got tails?
3
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5answers
204 views

Probability and the “out of” thing"

I have quite an odd question: I am not able to fully understand the concept of "out of". If I roll a dice once, from a total of $6$ possible outcomes, I'll get 1. Why does that mean a fraction ...
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0answers
15 views

Poisson process and probability

Let $N_t$ be a Poisson process and $T_{N_t}=X_1+\ldots+X_{N_t}$ where $X_i$ has an exponential law ($E(\lambda)$). Let $A_t=t-T_{N_t-1}$ and $B_t=T_{N_t}-t$. Show that for $x,y,t \geq 0$, $P(B_t \geq ...
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0answers
19 views

its about finding probability given the standard deviation [on hold]

for boys, the average number of absence in the first grade is 15 with a standard deviation of 7;for girls, the average of absence is 10 with standard deviation of 6. in nation wide survey, suppose 100 ...
0
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0answers
14 views

Combining n simultaneously occuring probabilities of an event occuring into one summative probability

I am a bit lost with regards to the problem described a bit further down, because though many methods to approach it are documented in available literature, the verdict as to which model is the most ...
0
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1answer
12 views

Is $P(W \geq z |V \geq y)=P(U-V \geq z |V \geq y)=P(U \geq z+y)$ correct?

Let $U,V,W=U-V$ random variables with $z,y \geq 0$ $$P(W \geq z |V \geq y)=P(U-V \geq z |V \geq y)=P(U \geq z+y)$$ Is it correct?
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1answer
13 views

Probability distribution of the difference of two random variables

Let $X,Y,$ and $Z$ be random variables, with $Z=X-Y$ and $z,y \geq 0$ $$P(Z \geq z, Y \geq y)=P(X-Y \geq z, Y \geq y)=P(X \geq y+z)$$ Is that correct? Thank you
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0answers
19 views

probability combination

McGyver is faced with the problem of opening a safe with 10 buttons numbered from 0 to 9. The safe can be opened by pressing three buttons, not necessarily distinct, in correct order. Realizing that ...
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0answers
18 views

In a sweepstakes giveaway scenario, how does having 2 chances to win the same prize affect the overall odds?

In a sweepstakes giveaway scenario where total entries are expected to result in final odds of 1:93,150.685 for/against a single entrant (after adjusting for multiple entries) and can be won by either ...
0
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1answer
20 views

Expected error of simplifying to a geometric distribution

While reading an answer related to solving a problem with a geometric distribution, the following question occurred to me. The answer gives two possibilities for replying the OP's question. In the ...
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0answers
12 views

Maximising returns Limiting Risk

This is probably a simple question/solution, but I'm no math expert. I'm looking into a Facebook group that provides bet to try and get up to 50k, you may have heard of it. The premise being that you ...
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0answers
26 views

Is the density of an absolutely continuous distribution necessarily unique? [on hold]

Is the density of an absolutely continuous distribution necessarily unique?
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0answers
39 views

Concentration inequality for sum of squares of i.i.d. sub-exponential random variables?

Suppose $X_1, X_2, \ldots, X_n$ are independent and each has the same distribution with a sub-exponential random variable $X$ (for example, $X$ is the square of a standard normal Gaussian variable). ...
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0answers
32 views

Find the minimum number of tickets to guarantee the win of a n-bit binary lottery?

Here's the problem. I just don't know how to approach it. If the 'one error tolerance' were removed, then this would be a simple binomial distribution problem. But now I can't figure it out. In ...