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 ...

learn more… | top users | synonyms (2)

2
votes
2answers
13 views

Probability and with replacement sampling

I'm reading the book "Model Assisted Survey Sampling" from Sรคrndal et al. In chapter 2, there's a section about Sampling with replacement. I'll put this into context: We have $m$ independent draws, ...
1
vote
0answers
12 views

The average rate of job submissions in a busy computer center is 4 per minute.

If it can be assumed that the number of submissions per minute interval is Poisson distributed, calculate the probability that (a) at least two jobs will be submitted in any minute $P(X\geq 2)$ so ...
0
votes
0answers
3 views

Correlation Coefficient in Latent Dirichlet Allocation

Can I use Correlation Coefficient to describe the relationship between two words in LDA? I know JS and KL divergence can give me the similarity between two words but can the similarity given from the ...
0
votes
1answer
18 views

Invalid given probability question?

My math textbook asks: Two fair dice are tossed. Find each probability. $P($less than $5$ or greater than $3)$ After doing some math: $P($sum of less than $5$ or greater than $3)=P($sum less than ...
-4
votes
0answers
16 views

Could an average number misrepresent a likely scenario if there is no limit on one end?

Boggling myself over this question since a friend asked me it. If you are trying to calculate your probability of sucess on a system from 0 to infinity on say a 1% rate of sucess with no failure cap. ...
0
votes
0answers
19 views

Acceptance Sampling - Random Access Memory Chips

Random access memory chips are packed in batches of $1000$. A sample of size $15$ is randomly selected from each batch and subjected to tests of reliability. The batch is accepted if the sample ...
0
votes
1answer
13 views

Question about the support of a joint distribution

Let X and Y be continuous random variables having the joint pdf $$f(x,y) = 8xy , 0\leq{y}\leq{x}\leq{1}$$ Find $g(x|y=\frac{1}{2})$ the conditional pdf of $X$ given $Y = \frac{1}{2}$ I found that ...
0
votes
1answer
21 views

Power function exponential distribution

I am trying to find the power function for a test. I know that the power function is calculated by $\beta(0) = P_0(x \in R)$ where $R$ is the rejection region. What I know about this test is that $X ...
0
votes
1answer
9 views

Iterated Bayesian Updates

I get a sequence of data that is generated by a distribution with parameter $a_0$ (e.g. $\mathcal{N}(a_0,1)$). I assume a prior distribution $P(a)$, and Bayesian update for the belief according to the ...
0
votes
1answer
28 views

Proving $\displaystyle P(A|B \ \mathrm{and} \ C) = \frac{P(A|C)P(B|A \ \mathrm{and} \ C)}{P(B|C)}$

Problem Prove that $\displaystyle P(A \mid B \cap C) = \frac{P(A\mid C) \cdot P(B\mid A \cap C)}{P(B\mid C)}$. Thoughts I'm having some trouble interpreting $\displaystyle P(A\mid B \cap C)$, and ...
0
votes
3answers
32 views

Independence and expected value

I have a theorem that says If two random variables $X,Y$ are independent, then for any non-negative measurable functions $f:E\to\mathbb{R}$ and $g:E\to\mathbb{R}$ the following holds ...
0
votes
2answers
36 views

What does P(X=Y) mean?

Let X and Y be binary random variables, with $P(X = 0) = 1/4$, $P(Y = 0) = 1/4$ and $P(X = Y) = 1/2$ I want to calculate $P(X=x,Y=y)$ (i.e. probability of x and y) and P(X=x|Y=y) for all all x and y. ...
1
vote
1answer
13 views

Maximal deviation from mean of a bounded random variable

Is there a non-probabilistic Hoeffding like inequality which tells me the deviation between a bounded random variable and its expectation? Let $X$ be a random vector such that $||X|| \leq c$. I am ...
0
votes
0answers
34 views

$N = Poisson(\lambda)$, $\{U_i\}$ iid $\implies (N_1, N_2) = Po(\lambda p_1)$x $Po(\lambda p_2)$

Let $\{N\}\cup\{U_i\}$ be independent random variables. $N = $ Poisson$(\lambda)$ $\{U_i\}$ iid, taking values in $\{1,2\}$, $\mathbb{P}[U_i = 1] = p_1$ and $\mathbb{P}[U_i = 2] = p_2$, $p_1 + p_2 ...
0
votes
0answers
10 views

Probability based time estimates

I was handed a problem today that got me thinking there has to be a better way, so I'm asking you fine folks for a more elegant way to solve this problem. It involves time estimation to complete a ...
1
vote
1answer
42 views

Every morning the lecturer chooses pairs of students

There are 10 students in a class 7 males and 3 female. Every morning the lecturer chooses pairs of students in a random. X - numbets of teams, including a man and a woman (together) I thought ...
0
votes
0answers
22 views

What is an upper bound for $\|E(X|\mathcal{A})-E(X)\|$?

Let $X$ be a random element in a Banach space with norm $\|\cdot\|$, and $\mathcal{A}$ be a $\sigma$-algebra. What is an upper bound for $\|E(X|\mathcal{A})-E(X)\|$? Existing results: It has been ...
1
vote
1answer
30 views

Combining mean-values.

Suppose I have machine that solves a certain type of problem in time T. T is not the same every time but depend upon a probability distribution $p(T)$. The average time $\langle{T}\rangle$ is ...
0
votes
0answers
38 views

Expected value and sum of independent variables.

EDIT: I've found my mistake. Flipped around the values because in my head I had them tails up at the start.. Not sure what to do with the question now... On a table there are three coins in a row, ...
4
votes
2answers
111 views

Can someone explain what a portfolio is in financial math?

I took mathematical probability last semester and now I am taking financial mathematics, but only probability was a pre requisite for financial math (no finance classes were required). These types of ...
0
votes
2answers
30 views

Optimization of a function over probability distributions

I'm trying to solve certain optimization problems dealing with probability distributions. Consider the space of probability distributions $\{ 1, ..., N\} \to [0, 1]$ I have a function $f : (\{ 1, ...
6
votes
2answers
30 views

lottery to pick a group while respecting pairs

I am running an event that will be oversubscribed, so I'd like to use a lottery to randomly pick the participants that will be accepted. (For example, 29 people want to attend, but I can accommodate ...
0
votes
0answers
16 views

Prove that a function is single peaked

Consider the following function: $$F(K)=\sum_{i=K+1}^{M} P(i,M) - \delta K P(K,M),$$ where $K,M\in \mathbb{N}$, $K<M/2$, $0<\delta,p<1$ and $P(i,M) = \binom{M}{i}p^i(1-p)^{M-i}$. I want to ...
0
votes
1answer
22 views

Probability of 1 trial getting 8 or more heads/tails in 10 trials of 10 flips

I was recently reading a book on probability "Drunkard's Walk: How Randomness Rules Our Lives" and there is a probability problem below that I cannot seem to replicate: "if each of 10 Hollywood ...
0
votes
0answers
38 views

Let (X, Y ) be uniformly chosen on the square region {(x, y) : |x| + |y| < 1}.

What is the density of (X,Y)? What is the distribution function of the angle 0 < ฮ˜ < 2ฯ€ made between the positive x-axis and the ray connecting the origin to the point (X, Y)? What is the ...
0
votes
1answer
22 views

Chances for $3$ 6-sided die and $2$ 8-sided die to have a sum of $12$

If $5$ dice are rolled, $3$ 6-sided die and $2$ 8-sided die, how do I come up with the chances that the sum will be $12$? I've figured that there are $13824$ total combinations, but can't figure out ...
4
votes
4answers
158 views
+50

Die that never rolls the same number consecutively

Suppose we have a "magic" die $[1-6]$ that never rolls the same number consecutively. That means you will never find the same number repeated in a row. Now let's suppose that we roll this die $1000$ ...
-9
votes
0answers
39 views

How to solve Probability? [on hold]

An urn contain 3 red and 5 green balls. Two balls are selected from the urn without replacement . Calculate the probability that i) Both balls are green ii) The second ball is green
-1
votes
0answers
17 views

Poisson problem to get exact probability distribution [on hold]

A gas utilization machine at the Exxon plant down the road receives occasional random shocks, at a Poisson rate of one shock per month. The machne will blow up precisely after receiving the 60th ...
-9
votes
1answer
50 views

How to Solve a Probability? [on hold]

Your neighbour has 2 children. You learn that he has a son , named Joe. What is the probability that Joeโ€™s sibling is a brother?
0
votes
1answer
19 views

Probability of exit from compact set

I have a continuous real valued diffusion $\{ X_t \}_{t\ge0 }$ that is contained in a compact set $[a,b] $of $\mathbb{R}$, where $a > 0$ and. Define the stopping times \begin{equation} \tau_c=\inf ...
2
votes
2answers
35 views

How to answer this poisson distribution?

Writer is writing a book and he is doing 2 mistakes per page What is the probability that the 2nd mistake of the writer is in page 3? What I tried to do is as follows: $X$~$Poi(2)$ -> 2 mistakes ...
6
votes
0answers
41 views

Exponential is to Poisson as Normal is to ???

In a time series, if the gap between successive events follows an exponential distribution with PDF $\lambda e^{-\lambda}$, then a Poisson distribution with parameter $\lambda$ tells you the ...
2
votes
1answer
15 views

Probability in selected group

35% of students are female. We know that if we select 20 from 200 students there are first 5 students who are male. What is a probability that 6th one is also male? First of all, I don't know if ...
2
votes
1answer
19 views

Sampling from Bivariate Normal, Relation between two coordinates

Suppose the mean and covariance matrix of a bivariate normal distribution are respectively $(0,0)$ and $\begin{pmatrix}a^2 & c \\ c & b^2\end{pmatrix}$. Let $(x_1,~ x_2)$ be a datapoint ...
0
votes
1answer
74 views

Definition of a random variable $\mathrm{Var}(X)$

So $\mathrm{Var}(X) = \mathrm{E}((X-\mu)^2)$, but how can you subtract a function $(X)$ by a value ($\mu)$? And does it make sense to square a function?
-2
votes
1answer
33 views

How do can i solve the integral, finding cdf [on hold]

Let $X$ be an exponential random variable with mean 1 and Y a uniform random variable between $0$ and $1$. Assume X and Y are independent and let $Z =e^{X/2}$ Find the joint cumulative ...
0
votes
1answer
32 views

Sum of random variables goes to infinity

I'm trying to show the following: Let $(X_n)_{n\in\mathbb{N}}$ be a sequence of i.i.d random variables with $\mathbb{E}[|X_1|]<\infty$ and $\mathbb{E}[X_1]=\mu$. Consider ...
0
votes
0answers
24 views

Probability with ordered statistics and exponential distribution involved

Assume that $X_1,X_2$ are independent random variables with exponential distribution with the same mean 100. Let $X_{(1)}=\min\{X_1,X_2\}$ and $X_{(2)}=\max\{X_1,X_2\}$. Calculate ...
0
votes
3answers
35 views

joint density function of two independent random variables

Suppose that $๐‘‹_1$ and $๐‘‹_2$ are independent and follow a uniform distribution over $[0, 1]$. Let $๐‘Œ_1 = ๐‘‹_1 + ๐‘‹_2$, and $๐‘Œ_2 = ๐‘‹_2 โˆ’ ๐‘‹_1$. a) Find the joint pdf $๐‘“_{๐‘Œ_1,๐‘Œ_2} (๐‘ฆ_1, ๐‘ฆ_2)$ ...
0
votes
0answers
20 views

Integal involving Normal and Log-normal PDF/CDF

I am following this example where the idea is to compute the failure probability using different approaches. The problem is given at the beginning. We have two random variables $R$ and $F$, following ...
1
vote
0answers
17 views

issue on conditional-expectation with crossed filtration

Why we have this equality ? $$\mathbb{E}[\ \mathbb{\hat{E}}(X(.)|\mathcal{F}_t)_G K(G) |\mathcal{F}_t] = \int_{\mathbb{R}}\mathbb{\hat{E}}(X(.)|\hat{\mathcal{F}}_t)_u K(u) dP_t^G(u)$$ For all ...
3
votes
2answers
30 views

An average of three calls arrive every $5$ min. Find the probability that exactly four calls will arrive during a $5$ minute interval.

An average of three calls arrive every $5$ min. Assuming a Poisson arrival rate, compute the probabilities of the following events: (a) exactly four calls will arrive during a $5$ minute interval. ...
1
vote
1answer
23 views

Find the conditional pmf of $Y$ given $X = 0$

Let $X$ and $Y$ have the joint pmf defined by $f(0, 0) = f(1, 2) = 0.3$, $f(0, 1) = f(1, 1) =0.2$ $(a)$ Tabulate the conditional pmf of $Y$ given $X=0$ $(b)$ Tabulate the conditional pmf of $X$ ...
0
votes
2answers
46 views

Number of outcomes with 3 distinct numbers rolling 4 dice.

Suppose you roll 4 distinct dice. I am trying to find: a) The number of outcomes with 3 distinct numbers b) The number of outcomes with 2 distinct numbers I just want to check that my reasoning is ...
0
votes
1answer
30 views

Mean value for a simple random variable

From a box with numbers from 1 to 90, 6 numbers are extracted without reintroduction. To play this "game", you have to pay 1 and you win 15 millions if you predict the 6 numbers (nothing in all the ...
1
vote
0answers
29 views

Specific Radon-Nikodym Derivative Interpretation

Suppose $(\Omega, \mathcal{F}, P)$ and $(\Omega, \mathcal{F}, Q)$ are two probability spaces. The Radon-Nikodym theory says that if $P$ is absolutely continuous with respect to $Q$, then there exists ...
0
votes
1answer
31 views

Calculating the mean and variance of continuous distribution

The main question was "A machine produces 2mm to 12mm usb sticks. Any usb greater than 10mm in size will need to be thrown away." Part A) Calculate the portion that needs to be thrown away, and I got ...
1
vote
2answers
37 views

Probability Proof about A and B

I have to formally prove that: $$P(A) = P(A\wedge \neg B) + P(A\wedge B)$$ so I did like this: $$P(A\wedge \neg B) + P(A\wedge B)$$ $$=P(A\wedge \neg B) + P(A)\cdot P(B)$$ $$=P(A)\cdot P(\neg B) + ...
3
votes
1answer
58 views
+50

Integrating a probability density function that only depends on the norm

I have a probability density function $f$ on $\mathbb{R}^3$ which only depends on the norm of a vector (that is, it takes the same value for $x,y$ if their length is equal). Let me call a region of ...