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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2
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3answers
124 views

Two riflemen A and B shoot at a target simultaneously. A has a 0.8 chance of hitting and B has a 0.9 chance

What is the probability that the target will be hit? Assume independence. $P( X\ge 1) $ is the probability that the target will be hit at least once The complement is $P(X = 0)$, probability that the ...
1
vote
2answers
58 views

If $P(E_n) = 0$, then $P(\cup E_n) =0$

What does this question mean here. If the probability of $E_n$ is zero does that mean $p(E_i) =0, i < n$? I am not sure if I should assume subset here?
0
votes
1answer
194 views

How to determine significance of a binomial test on a sample

I'm looking to determine the significance of the result of a binomial test of a sample of a population. Example: Given a group of 10,000 people, I ask 1,000 if they prefer iOS or android. 550 respond ...
-1
votes
2answers
122 views

Joint Density Function Example

f(x,y)= $\frac 1y$ for 0 < x < y <1 f(x,y)= 0 elsewhere find P(x+y>.5): $\iint$ $\frac 1y$ dxdy I basically can't figure out the limits, since x and y are not only dependent on each ...
1
vote
1answer
88 views

A Tale of Urns and Balls

I got the following situation: 2 urns with 2 whites and 3 blacks 2 urns with 1 white and 4 blacks 1 urn with 4 whites and 1 blacks A ball is drawn from an urn (and this urn is selected at random). ...
3
votes
1answer
584 views

Independence of a random variable $X$ from itself

In our lecture on probability, my professor made the comment that "a random variable X is not independent from itself." (Here he was specifically talking about discrete random variables.) I asked him ...
1
vote
1answer
42 views

Simple stats question A level help

I've not done stats in a while and struggling with simple questions like these. Can anyone help? The probability that Adam will pass the hard examination is 0.12. The probability that Brian will pass ...
5
votes
1answer
166 views

Surprising limit (probability of no two coinciding pairs)

I stumbled upon this question by random chance. The motivation is kind of long, the question is pretty short; if you're just here for the limits, feel free to skip to the break. I'm taking five ...
0
votes
1answer
59 views

Basic Probability Question: Ordered Sample With Replacement (Help!)

Each time a fair die is tossed a marker is moved 10 cm east, west, north or south if the die shows 1, 2, 3, or 4 respectively. If the die shows a 5 or a 6 the marker is not moved. What is the ...
0
votes
2answers
117 views

Is there a random variable where E[X] exists but the expectation of the negative and positive part do not?

Is there a random variable where $E[X]$ exists but the expectation $E[X^{+}]$ and $E[X^{-}]$ do not? If not, how can I show this? I know that it is usually written that $$ X = X^{+} - X^{-}$$ and ...
-1
votes
5answers
5k views

Probability - exactly one of A and B occurs

$A$ and $B$ are events that are subsets of the sample space. $C$ is the event that exactly one of $A$ and $B$ occurs. 1) Write an expression for $C$ in terms of unions, intersections and complements ...
0
votes
3answers
44 views

distant land Probability Question

In a distant land, parents continue to have children until they have a girl and then they stop having kids. Assume there is no limit to the number of births possible to each couple. (a) What is the ...
0
votes
1answer
54 views

Can $A^{c} \cap B^{c} = A^{c} - (A^{c} \cap B)$?

Can $A^{c} \cap B^{c} = A^{c} - (A^{c} \cap B)$? I am using this identity to prove the probabilities for $A^{c}$ and $B^{c} $ are independent, given those for $A$ and $B$ are independent. Is there ...
6
votes
2answers
278 views

Interview Puzzle

Suppose $5$ blue points and $5$ red points are selected in the interval $[0,1]$. What is the probability that the points will interleave each other? Interleave as in one blue point followed by one red ...
0
votes
1answer
101 views

Why the result of probability density function of a random variable is greater than 1?

For a normal random variable with mean 0.3 and standard deviation 0.03, its PDF would be as follows (I used MATLAB to draw it): My first question is that why these probabilities are larger than 1? ...
5
votes
3answers
1k views

Expected max load with $n$ balls in $n$ bins?

If you throw $n$ balls into $n$ bins uniformly and independently at random, let $X$ be the number of balls in the bin with the largest number of balls in it. Is there an elementary way to ...
1
vote
2answers
287 views

“by definition A and B R.V are independent means that: $p(A∪B)=p(A)+p(B)$ right?” No, absolutely not right.

Can someone please explain why? Isn't $p(a,b)=p(a)*p(b) $ equivalent to $p(A∪B)=p(A)+p(B)$? If not can you please give a counterexample or something? Thanks a lot!
3
votes
1answer
172 views

Interchanging probability and limits

I am trying to prove that $\mathbb{P}(\cup A_n)=1$ if $\mathbb{P}(\limsup A_n)=1$ when $A_1...A_n$ are independent events and $\mathbb{P}(A_n)<1$. My question is, while trying to prove this, can I ...
0
votes
1answer
452 views

Rolling Dice Repeatedly

This question is from DEGROOT's PROBABILITY and STATISTICS. Rolling Dice Repeatedly: Suppose that two dice are to be rolled repeatedly and the sum $T$ of the two numbers is to be observed for each ...
0
votes
1answer
52 views

Quick probability question regarding not-so-obvious answer

Consider an experiment that consists of determining the type of job, either blue- collar or white-collar, and the political affiliation, Republican, Democratic, or Independent, of the 15 members of an ...
0
votes
1answer
68 views

probability density

You throw a dart randomly at a board of radius 12 inches. If it lands within 4 inches of the center you get 3 points, if between 4 and 8 inches you get 2 points, and you get one point otherwise (call ...
0
votes
2answers
76 views

Poisson random variable. Average 1.2 per week, in 52 weeks, chance of 4 or more in a week?

Suppose weekly number of fatal traffic accidents in a large city is a Poisson random variable with an average of 1.2 per week. During the next year ( 52 weeks), what is the probability that there is ...
-1
votes
1answer
861 views

A fair coin is tossed until both heads and tails apear [closed]

A fair coin is tossed until both heads and tails have been obtained. Let x = the number of tosses needed (for example, if the sequence of tosses is HHT, then x = 3; If the sequence is TTTTTH, then x = ...
2
votes
1answer
125 views

I.I.D what does this stand for?

So almost everywhere in the book it's written "random variables are IID", what does this mean? I think it means independent and identically distributed but not sure. So by definition A and B R.V are ...
1
vote
1answer
185 views

CDF from generating function

Is there a way to obtain the CDF of a discrete random variable directly from one of its generating functions?
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votes
2answers
10k views

odds of rolling the same number, 5 times in a row?

Given a 6 sided die, what is the formula to work out the odds of rolling the same number, 5 times in a row?
3
votes
2answers
98 views

What is the probability of a continuous uniform random variable in $[0,1]$ to be $1/2$?

Suppose I have a random variable $x$ with uniform pdf over $[0,1]$. When I evaluated the probability $P(x=1/2)$, I got 0. How can that be correct? After all the probability exists and is equally ...
4
votes
3answers
675 views

Probability of drawing all red balls before any green ball

Question: Suppose that a box contains $r$ red balls, $g$ green balls, and $b$ blue balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. What is the ...
0
votes
1answer
108 views

Conditional density of transformation of Gaussian Random variable

Suppose we know the conditional density of $X \vert Z$, where ($X,Z$) are jointly Gaussian, with $Z$ a non degenerate Gaussian random vector with $m$ components. Suppose $Z=AY$ where where ($X,Y$) are ...
0
votes
2answers
359 views

Finding expected perimeter and area of rectangle using random distribution

Hi i have a question: A random rectangle is formed in the following way- Base X is generated from Gamma(1, λ) distribution and after generating the base, the height Y is chosen uniformly on the ...
0
votes
3answers
73 views

Is being mutually exclusive and independent is the same thing?

If i say 2 events are mutually exclusive ,is it the same thing saying that they two are independent of each other?
0
votes
1answer
317 views

expectation of Gamma distribution help

If x∼Gamma(1,λ) how would i find the expected value E(e^bx) where b=aλ I'm kinda stuck as to how to approach the question. Some help will be greatly appreciated Thank you in advance
0
votes
1answer
224 views

expectation calculation in probability and statistics

2 four-sided dice are rolled. X = number of odd dice Y = number of even dice Z = number of dice showing 1 or 2 So each of X, Y, Z only takes on the values 0, 1, 2. (a) joint p.m.f. of (X,Y)? joint ...
0
votes
2answers
79 views

Probability of winning this game

This is adapted from a little game I've played recently: Suppose that every day you get to select one sealed box out of nine and collect whatever item is in the box. How the $n>9$ items are placed ...
0
votes
1answer
31 views

Conditional Expectation of $M_n$ given $F_n$

Why is that the Conditional Expectation of $M_n$ given $F_n$ is equal to $M_n$ where $M_n$ is collection of the random variable $X_i$ where i runs from 0 to n and $F_n$ is the filtration at time n?
0
votes
2answers
81 views

Dice sum probability

Simulate two separate dice (use random numbers with the appropriate range) being rolled 10 times. What are the percentage of rolls that resulted in a sum of 7, a sum of 2 and a sum of 11. I came ...
4
votes
1answer
918 views

probability of flipping a total of 20 heads before flipping 10 tails in a row?

I want to find the probability that I will flip a fair coin and get $10$ heads in a row before I flip a total of $20$ tails. Or the opposite, the probability that I will flip a total of $20$ heads ...
2
votes
1answer
403 views

How to calculate the expected value of number of two consecutive zeros in a randomly-generated binary string?

There is a bitmap which has m bits. Initially, all m bits are zeros. There are n random number generators which can generate random integers between 1 and m uniformly. Usually, n is larger than m. ...
0
votes
1answer
64 views

what is the meaning to evaluate the variance of probability destribution for insurance in general?

what is the meaning to evaluate the variance of probability destribution for insurance in general? What does it do(setting the price, estimate cash reserve or else), also does evaluate the variance ...
0
votes
3answers
116 views

Homework on Binomial Distribution

I have another homework, and I don't get this particular sub-question. I need to understand it. I don't know what I'm supposed to do. For the sake of brevity, I won't post the entire problem. ...
0
votes
1answer
63 views

Probability and Card drawing

I got a deck with 10 red cards and 30 black cards. Now, I draw a couple of cards 20 times. I draw the couple without replacement, but the 20 drawings of couples are with replacement (I restore the ...
-1
votes
2answers
316 views

Mean and variance calculation

An unfair coin has probability $p$ of heads. I flip it until I get heads, then I flip it some more until I get tails. Let $X$ be the total number of flips. So here are some possible outcomes: HT : $X = ...
0
votes
1answer
55 views

Approximation of a standard normal random variable in probability

Let $Z$ be standard normal random variable and $(a_n)_{n\in\mathbb{N}}$ a real sequence with $a_n\xrightarrow{n\rightarrow\infty}\infty$. Can we obtain something like $$P(Z>a_n)\leq \exp(- c_n)$$ ...
3
votes
1answer
154 views

Connection between Normal,Gamma and beta distribution

if $X,Y,Z\sim {N}(0,1)$ then $(X^2+Y^2+Z^2)\sim \text{Gamma} (0.5\cdot 3 , 0.5)=\text{Gamma} (1.5,0.5)$ Also, we define $T$, such that $T= \frac{X^2 }{ X^2+Y^2+Z^2} $ I don't understand why then ...
1
vote
1answer
97 views

Beginner question: Available space in a warehouse

I have a year's worth of data for the available slots in a warehouse. There is a data point for every minute of the year. timestamp available slots The data seems to follow a certain pattern, ...
1
vote
3answers
1k views

Probability question of hats

Five bald men wearing hats go to a party, and when they arrived they put their hats in a dark closet. During the party, someone yells, “Fire!” and the men rush to the closet, grab a hat at random, and ...
0
votes
2answers
560 views

Finding the distribution of a poisson distribution with random variable lambda

So suppose $X$ is a rv with a Poisson distribution with $\lambda$ being a random variable as well. $\lambda$ has an exponential distribution with mean $1/c$ and $f_\lambda(t) = c\times\exp(-ct)1_{[0, ...
1
vote
2answers
137 views

what is the probability of choosing $m$ numbers from the interval $[0,1]$

As far as I know there are infinitely many real numbers between $[0,1]\subseteq R$, what is the probability of choosing a given set of numbers $\{x_1,...,x_m\}$ where $x_i\in[0,1]$ from $[0,1]$? where ...
1
vote
2answers
709 views

Probability of Independent Events Happening at least twice

If the probability of hitting a target is $1/5$ and ten shots are fired independently, what is the probability of the target being hit at least twice? Would it be $$1 - \left[\left(\frac 1 ...
1
vote
1answer
560 views

Valid values of constant for probability mass function (PMF)

For what values of constant $c$ do the following functions define a valid PMF for random variable $X$ on supports $X=\{1,2,...\}$ (1) $f(x) = c/2^x$ (2) $f(x) = c2^x/x!$ I was thinking ...